V 


PRACTICAL   PHYSICS 


THE  MACMILLAN  COMPANY 

NEW  YORK    •    BOSTON   •    CHICAGO  •    DALLAS 
ATLANTA    •    SAN    FRANCISCO 

MACMILLAN   &   CO.,  LIMITED 

LONDON    •    BOMBAY   •    CALCUTTA 
MELBOURNE 

THE  MACMILLAN  CO.  OF  CANADA,  LTD. 

TORONTO 


PRACTICAL    PHYSICS 


FUNDAMENTAL  PRINCIPLES  AND 
APPLICATIONS    TO    DAILY    LIFE 


N.   HENRY   BLACK,   A.M. 

SCIENCE  MASTER,   BOXBURY  LATIN  SCHOOL 
BOSTON,  MASS. 

AND 

HARVEY   N.   DAVIS,   PH.D. 

PROFESSOR  OF  MECHANICAL  ENGINEERING 
HARVARD  UNIVERSITY 


REVISED  EDITION 


fiotfe 

THE   MACMILLAN   COMPANY 
1922 

All  rights  reserved 


V  •   ^«"-«    '«••  *      .*    'BWNTEb  dV-TyE^NITED  STATES 


OF  AMERICA 


COPYRIGHT,  1913,  1922, 
BY  THE  MACMILLAN  COMPANY. 


Set  up  and  electrotyped.     Published  May,  1922. 


Norfooott  tynss 

J.  S.  Gushing  Co.  — Berwick  &  Smith  Co. 
Norwood,  Mass.,  U.S.A. 


PREFACE 

THE  chief  aim  of  the  first  edition  of  this  book  was  to  impress 
upon  teacher  and  pupil  alike  that  the  study  of  physics  is  not 
merely  an  abstract  mental  exercise  to  be  patiently  undergone 
in  the  hope  of  training  one's  mind.  It  is  rather  a  simple, 
straightforward  attempt  to  understand  and  to  use  intelligently 
a  multitude  of  familiar  objects  and  devices  that  surround  us  on 
every  hand.  If  rightly  taught,  physics  should  be  the  most 
popular  subject  in  the  curriculum ;  for  no  satisfaction  is  more 
complete  than  that  which  comes  to  a  person  already  familiar 
with  the  fundamental  principles  of  some  branch  of  modern 
science  who  finds  himself  habitually  and  instinctively  detect- 
ing and  appreciating  applications  of  these  principles  in  unex- 
pected places  in  the  course  of  his  daily  life. 

It  was  to  suggest  this  point  of  view  that  we  chose  the  title 
PRACTICAL  PHYSICS  ;  and  the  same  considerations  led  us  to  di- 
rect the  student's  attention  chiefly  to  the  familiar  objects  of 
everyday  life  rather  than  to  the  subtleties  of  molecular  physics 
and  atomic  structure.  Although  the  latter  are  of  the  greatest 
importance  and  interest  to  maturer  students,  they  are  never- 
theless so  far  outside  the  experience  of  those  who  are  approach- 
ing the  subject  for  the  first  time  as  to  seem  inevitably  more 
like  "book  learning "  than  like  real  life. 

We  have  pursued  the  same  course  in  the  present  revision. 
In  particular  we  have  been  responsive  to  the  fact  that  during 
the  nine  years  since  the  first  edition  appeared,  the  automobile 
has  ceased  to  be  largely  the  plaything  of  the  well-to-do,  and 
has  become  the  working  tool  of  multitudes  of  families  in  city 
and  country  alike.  As  illustrative  material  for  nearly  every 
division  of  physics  the  modern  automobile  is  especially  appro- 
priate because  of  this  widespread  familiarity  on  which  a  physics 
teacher  can  build. 

483234 


VI  PREFACE  . 

The  World  War  has  had  many  notable  results,  not  the  least 
important  of  which  are :  first,  that  it  awakened  a  popular 
interest  in  and  appreciation  of  physical  and  chemical  science 
hitherto  unmatched  in  the  world's  history ;  and  second,  that  it 
led  to  an  unparalleled  concentration  of  able  minds  on  practical 
or  applied  as  distinguished  from  pure  or  theoretical  physics 
and  chemistry.  There  resulted  many  new  applications  of  the 
fundamental  principles  of  these  sciences.  Of  these  we  have 
attempted  to  describe  only  such  as  seemed  to  us  important 
in  peace  as  well  as  in  war ;  but  even  the  few  selected  form  an 
important  addition  to  the  domain  of  " practical  physics." 

We  have  doubtless  included  in  this  book  more  material  than 
it  is  advisable  for  any  class  to  undertake  in  a  single  year.  This 
gives  the  teacher  an  opportunity  to  adapt  his  instruction  to 
local  needs  and  to  the  time  available.  We  believe  that  it  is 
most  important  to  select  carefully  just  what  material  can  best 
be  used  and  to  teach  that  thoroughly,  rather  than  to  try  to  touch 
upon  many  topics  superficially. 

The  present  edition  is  as  nearly  like  our  former  book  in  spirit, 
pedagogical  method,  and  general  content  as  the  passage  of 
nine  years  permits.  In  particular,  we  have  tried  to  arrange 
the  material  in  the  most  teachable  order,  to  give  clear  and  con- 
cise summaries  at  the  ends  of  the  chapters,  to  set  practical 
rather  than  artificial  problems,  to  minimize  the  arithmetical 
drudgery  involved  in  solving  them,  and  to  suggest  many  ques- 
tions designed  to  get  students  into  the  habit  of  seeking  useful 
information  from  the  mechanics,  artisans,  engineers,  and  others 
whom  they  meet  outside  the  classroom. 

In  the  details  there  are,  however,  a  number  of  improvements 
in  this  edition,  among  which  the  following  may  be  men- 
tioned . 

1.  There  are  about  one  hundred  more  illustrations,  and  more 
than  half  of  the  old  cuts  have  been  redrawn  for  greater  clearness 
and  simplicity. 

2.  The  applications  of  physical  principles  to  the  submarine, 


PREFACE  yii 

the  automobile,  the  airplane,  and  the  airship  have  been  more 
fully  discussed. 

3.  The  subject  of  electricity  has  been  handled  more  simply 
and  directly,  with  special  reference  to  its  present-day  commer- 
cial applications.     Radio  communication  and  radioactivity  have 
received  more  attention. 

4.  We  have  greatly  increased  the  number  of  problems  and 
questions,  not  expecting  that  all  will  be  done  by  any  class,  but  in 
order  to  offer  more  variety  and  greater  opportunity  for  selection. 

5.  We  have  introduced  a  considerable  number  of  "practical 
exercises. "     These  may,  of  course,  be  ignored  by  the  teacher 
without  disturbing  the  rest  of  the  course.     But  if  each  student's 
interest  can  be  so  aroused  that  he  undertakes  with  enthusiasm 
to  carry  one  or  more  of  these  independent  investigations  through 
to  some  definite  conclusion  in  the  course  of  the  year,  devoting 
spare  time  to  it  as  to  any  hobby,  and  using  his  own  initiative 
with  only  occasional  informal  guidance  from  the  teacher,  both 
his  pleasure  and  his  mental  gain  will  be  very  great. 

We  are  greatly  indebted  to  many  teachers  who  from  their 
experience  with  the  first  edition  have  made  valuable  criticisms 
and  suggestions  for  its  improvement.  Especially  would  we 
mention  Mr.  Edward  E.  Ford,  of  the  West  High  School,  Roches- 
ter, N.  Y.,  Mr.  Arthur  B.  Hussey,  of  the  High  School,  New 
Rochelle,  N.  Y.,  Mr.  A.  L.  Jordan,  of  the  Technical  High  School, 
San  Francisco,  Mr.  H.  W.  LeSourd,  of  Milton  Academy,  Mil- 
ton, Mass.,  Mr.  M.  R.  McElroy,  of  Woodward  High  School, 
Cincinnati,  and  Mr.  J.  C.  Packard,  of  the  High  School,  Brook- 
line,  Mass. 

In  obtaining  material  for  the  new  illustrations  we  have  been 
greatly  assisted  by  Professor  George  E.  Hale  of  Mt.  Wilson  Ob- 
servatory at  Pasadena,  Mr.  Walter  B.  Littlefield  of  Boston, 
Professor  Dayton  C.  Miller  of  the  Case  School,  Cleveland,  Pro- 
fessor Frank  A.  Waterman  of  Smith  College,  and  Professors 
Theodore  Lyman,  Lionel  S.  Marks,  and  Frederick  A.  Saunders 
of  Harvard  University. 


Vlll  PREFACE 

Among  the  firms  which  have  cooperated  with  us  in  preparing 
the  text  and  the  illustrations  are  the  following : 

Allen  Motor  Co.,  Columbus,  Ohio. 

Allis-Chalmers  Manufacturing  Co.,  Milwaukee,  Wis. 

Bishop  &  Babcock  Co.,  Cleveland,  Ohio. 

Blaw-Knox  Co.,  Pittsburgh,  Pa. 

S.  F.  Bowser  &  Co.,  Fort  Wayne,  Ind. 

Dayton  Money  weight  Scales,  Dayton,  Ohio. 

The  De  Laval  Separator  Co.,  New  York,  N.  Y. 

De  Laval  Steam  Turbine  Co.,  Trenton,  N.  J. 

Dodge  Brothers,  Detroit,  Mich. 

Eastman  Kodak  Co.,  Rochester,  N.  Y. 

Electric  Controller  &  Manufacturing  Co.,  Cleveland,  Ohio. 

Ford  Motor  Co.,  Highland  Park,  Mich. 

Fulton  Iron  Works,  St.  Louis,  Mo. 

General  Electric  Co.,  Schenectady,  N.  Y. 

Holt  Manufacturing  Co.,  Peoria,  111. 

Johns-Man ville  Co.,  New  York,  N.  Y. 

Nicholas  Power  Co.,  New  York,  N.  Y. 

North  East  Electric  Co.,  Rochester,  N.  Y. 

Riehle  Bros.  Testing  Machine  Co.,  Philadelphia,  Pa. 

Sears,  Roebuck  &  Co.,  Chicago,  111. 

Skinner  Engine  Co.,  Erie,  Pa. 

Studebaker  Corporation  of  America,  South  Bend,  Ind. 

Western  Electric  Co.,  Chicago,  111. 

Westinghouse  Electric  &  Manufacturing  Co.,  East  Pitts- 
burgh, Pa. 

Western  Electric  Instrument  Co.,  Newark,  N.  J. 

The  authors  are  under  special  obligations  to  Dr.  D.  O.  S. 
Lowell,  formerly  headmaster  of  the  Roxbury  Latin  School,  for 
reading  the  proof  sheets,  and  to  Mr.  James  S.  Conant  of  the 
Suffolk  Engraving  and  Electrotyping  Co.,  Cambridge,  for  pre- 
paring the  illustrations.  N  H  B 

APRIL,  1922. 


TABLE   OF   CONTENTS 

CHAPTER  PAGE 

I.  INTRODUCTION:    WEIGHTS  AND  MEASURES        .        .        .  1 

II.  SIMPLE  MACHINES      .         .        .,        .        .        ..        ...  15 

III.  MECHANICS  OF  LIQUIDS     .         .  •»        .        .        .  6(T 

IV.  MECHANICS  OF  GASES  v      .         .         .         .         ...  96 

V.  NON-PARALLEL  FORCES   *.        »'       .         .        .        .        .  12§ 

VI.  ELASTICITY  AND  STRENGTH  OF  MATERIALS        .         .         .  149 

VII.  ACCELERATED  MOTION       ....        .         .         .         .  158 

VIII.  THREE  LAWS  OF  MOTION  .         .         .         .    •      .  •       *        .  174 

IX.  POTENTIAL  AND  KINETIC  ENERGY      .        .        .        .        .  186 

X.  HEAT  —  EXPANSION  AND  TRANSMISSION     ....  194 

XI.  WATER,  ICE,  AND  STEAM    .         ....        .         .  226 

XII.  HEAT  ENGINES    .        .        .        .        .        .        .        .        .  255 

XIII.  MAGNETISM      •«•"•;'•".        .        .        .        .        .         .  281 

XIV.  STATIC  ELECTRICITY    .        .        .       "..       •        •        .        •  293 
XV.     ELECTRIC  CURRENTS 307 

XVI.     EFFECTS  OF  AN  ELECTRIC  CURRENT 337 

XVII.  INDUCED  CURRENTS    .        .        .        .      V       •        •        •  37° 

XVIII.  ALTERNATING  CURRENTS     .        .                 .        .        .         .  403 

XIX.  SOUND          .        .        .        .        ...      .        .        .        .  427 

XX.  ILLUMINATION:    LAMPS  AND  REFLECTORS  -.  463 

XXI.     LENSES  AND  OPTICAL  INSTRUMENTS 486 

XXII.     SPECTRA  AND  COLOR  . 516 

XXIII.  ELECTRIC  WAVES  :    ROENTGEN  RAYS  AND  RADIOACTIVITY  529 

INDEX  545 


IX 


PRACTICAL   PHYSICS 

CHAPTER  I 

INTRODUCTION:    WEIGHTS  AND  MEASURES 

Why  study  physics  —  content  and  divisions  —  physics 
involves  measurement  as  well  as  description  —  important 
units  in  English  and  metric  systems  —  density  —  units  of 
time. 

1.  Why  study  physics?  Everyone  has  had  something  to 
do  with  machines  of  one  sort  or  another  all  his  life.  In  the 
household  there  are  sewing  and  washing  machines,  vacuum 
cleaners,  and  phonographs.  On  farms  people  mow,  reap,  and 
thresh  grain  with  machines  which  are  often  drawn  by  mechan- 
ical horses  called  tractors ;  they  pump  water  with  windmills 
or  with  hot-air,  gasoline,  or  oil  engines ;  they  skim  milk  with 
a  machine  called  a  separator;  and  even  the  milking  itself  is 
often  done  by  machines.  In  the  city  people  travel  on  electric 
cars  and  go  upstairs  on  hydraulic  or  electric  elevators ;  streets 
and  homes  are  lighted  and  cookstoves  heated  by  electricity 
generated  by  great  machines  in  central  power  plants.  In 
business  and  in  commerce  people  are  constantly  using  steam, 
gas,  and  electric  engines,  cranes  and  derricks,  locomotives, 
ships,  and  trucks.  The  telephone,  the  automobile,  and  the 
motion-picture  machine,  which  are  now  familiar  objects,  are 
applications  of  the  principles  of  physics. 

Everyone  has  used  one  or  more  of  these  devices,  and  nearly 
everyone  has  at  times  wondered  and  perhaps  discovered  how 
some  of  them  work.  That  is,  almost  everyone  has  already 
begun  to  study  physics,  for  it  is  one  of  the  chief  aims  of  physics 

1 


2  INTRODUCTION;    WEIGHTS   AND   MEASURES 

to  discover  all  that  can  be  known  about  such  machines  as  have 
just  been  mentioned. 

2.  Physics  a  science.       The   sort  of  physics   that  will  be 
found  in  this  book  differs  from  the  sort  that  everyone  has 
been  unconsciously  studying  all  his  life,  chiefly  in  that  it  seeks 
to  answer  not  only  the  questions  "  why  "  and  "  how,"  but 
also  the  question  "  how  much."     It  is  only  when  we  begin 
to  measure  things  definitely  that  we  get  the  kind  of  informa- 
tion that  helps  us  to  use  them  to  the  best  advantage.     Thus 
everyone  knows  in  a  vague  way  that  an  automobile  goes  up  a 
hill  because  the  gasoline  which  is  burned  in  the  engine  makes 
it  turn  the  driving  wheels,  and  these  in  turn  push  against  the 
road,  if  it  is  not  too  slippery,  and  thus  propel  the  automobile. 
The  physicist,  when  he  had  thought  of  all  this,  would  go  on 
to  ask  himself  such  questions  as  "  How  much  gasoline  does 
it  take,  how  much  ought  it  to  take  under  ideal  conditions, 
and  what  becomes  of  the  difference?     How  much  force  must 
be  exerted  by  the  brakes  to  hold  the  automobile  on  a  hill,  how 
large  a  brake  surface  will  do  this,  and  how  strong  must  the 
brake  .rod  be?  "     When  he  can  answer  all  these  and  many 
other  questions,  he  is  in  a  position  to  use  his  machine  more 
effectively,  and  perhaps  to  improve  its  mechanism. 

3.  Divisions  of  physics.     The  object  of  studying  physics  is, 
then,  chiefly  to  learn  to  think  accurately  about  very  familiar 
things.     But  these  things  are  so  varied  in  kind  that  we  shall 
find  it  convenient  to  divide  the  whole  subject  into  five  divisipns: 
mechanics,  heat,  electricity,  sound,  and  light.     For  example, 
suppose  we  wanted  to  make  a  thorough  study  of  the  auto- 
mobile  (Fig.   1).     Under  mechanics,  we  should  study  about 
its  cranks,  gears,  levers,  pumps,  and  brakes,  including  their 
movements,  and  the  strength  of  the  material  of  their  con- 
struction;   under  heat,  the  engine,  carburetor,  and  radiator; 
under  electricity,  the  spark  plug,  spark  coil,  generator,  and 
battery;    under   sound,  the  horn  and  muffler;    and  finally, 
under  light,  the  lamps  and  their  reflectors  and  lenses.     In  a 


PHYSICS  BEGINS   WITH   MEASUREMENTS  3 

similar  way  it  might  be  shown  that  any  piece  of  modern  machin- 
ery, whether  it  is  an  automobile  or  a  locomotive,  a  motor 
boat  or  an  ocean  liner,  an  airplane  or  a  submarine  boat,  is 


Fig.  i.     Cross  section  of  an  automobile.     (Compare  with  Frontispiece.) 

not  only  an  embodiment  of  the  principles  of  physics,  but 
has  in  very  large  measure  been  made  possible  by  the  science 
of  physics. 

4.  Physics  begins  with  measurements.  At  the  very  outset 
we  may  well  recall  an  old  saying  of  Plato's :  "If  arithmetic, 
mensuration,  and  weighing  be  taken  away  from  any  art,  that 
which  remains  will  not  be  much."  In  the  laboratory  the  student 
will  learn  to  measure  many  different  kinds  of  things,  not  mainly 
for  the  sake  of  the  results  he  gets,  but  rather  that  all  through 
life  he  may  know  a  good  measurement  when  he  sees  one,  and 
may  be  able  to  discuss  accurately  and  with  confidence  the 
quantitative  problems  that  are  always  coming  up. 

It  is  well  to  remember  that  all  physical  measurements  are 
more  or  less  inaccurate,  and  that  the  degree  of  precision  to 
be  aimed  at  depends  on  the  purpose  of  the  measurement.  For 
example,  an  error  of  an  inch  in  determining  the  distance  be- 
tween two  milestones  is  a  much  less  serious  matter  than  an 


4  INTRODUCTION:    WEIGHTS  AND  MEASURES 

error  of  one  one-hundredth  of  an  inch  in  measuring  the  diameter 
of  an  automobile  bearing. 

5.  Units  of  measurement.  In  the  United  States  the  value 
of  things  that  are  bought  and  sold  is  measured  in  dollars  and 
cents.  Fortunately  this  system  of  money  is  made  on  the 
decimal  plan,  that  is,  in  multiples  of  ten.  Our  system  of 
weights  and  measures,  on  the  other  hand,  is  not  a  decimal 
system,  and  is  very  inconvenient.  Nevertheless,  since  the 
pound,  foot,  quart,  gallon,  and  bushel  are  still  in  general  use 
in  the  United  States  and  in  Great  Britain,  we  must  be  familiar 
with  them.  During  the. last  century  most  of  the  other  civilized 
nations  have  adopted  the  metric  system  of 
weights  and  measures,  in  which  the  relation 
of  the  units  is  expressed  in  multiples  of  ten. 
In  scientific  work  the  metric  system  is  almost 
universally  used  throughout  the  world,  because 
it  greatly  reduces  the  work  in  making  com- 
putations. Therefore  it  is  advisable  for  us 
to  become  proficient  in  the  use  of  both  the 
English  and  the  metric  system  of  weights  and 
measures. 

Fig.  2.    The    inter-      6.   Meter  and  yard.     The    meter   is  the 
Tht^is^nce^is  distance  between  two  lines  on  a  metal  bar 
measured  between  (Fig.  2)  which  is  preserved  in  the  vaults  of 
the   International   Bureau    of   Weights   and 
Measures  near  Paris.* 
Since  the  length  of  this  metal  bai  changes  a  little  with  the 
temperature,  the  distance  is  measured  at  the  temperature  of 
melting  ice.     A  very  accurate  copy  of  the  bar  is  deposited  in 
the  United  States  Bureau  of  Standards  in  Washington,  D.C., 
and  this  copy  is  the  legal  meter  of  the  United  States. 

*  It  was  originally  intended  that  the  meter  should  be  equal  to  one  ten-millionth 
part  of  the  distance  from  the  equator  to  either  pole  of  the  earth,  but  it  is  im- 
possible to  reproduce  an  accurate  copy  of  the  meter  on  the  basis  of  this  definition. 
Later  measurements  have  shown  that  the  "  mean  polar  quadrant "  of  the  earth  is 
about  10,002,100  meters. 


UNITS  OF  AREA 


In  the  United  States  the  yard  is  legally  defined  as  ff-Jy  of 
a  meter. 

7.  Some  important  units  of  length.  In  the  problems  of 
physics  we  shall  find  that  certain  units  of  length  are  very  fre- 
quently used.  These  are  given  in  the  following  table  and 
should  be  memorized : 


ENGLISH. 


UNITS  OF  LENGTH 

1  foot  (ft.)  =  12  inches  (in.) 
1  yard  (yd.)  =  3  feet 
1  mile  (mi.)  =  5280  feet 


CENTIMETERS 
012 


MM   i 

123 
Relative  sizes  of  the  inch  and  the  centimeter. 


.c 


MM 

0  INCHES 

Fig-  3- 
METRIC. 

1  meter  (m.)  =  1000  millimeters  (mm.) 

1  meter  =  100  centimeters  (cm.)^    . 3^ 
1  kilometer  (km.)  =  lOO^meters          ?£:£*' 
1  inch  =  <27£40  centimeters  (Fig.  3) 
1  meter  =  39.37  inches 

8.  Units  of  area.  The  unit  of  area  which  is  most  extensively 
used  is  the  area  of  a  square  whose  side  is  of  unit  length.  Thus 
the  area  of  a  city  house  lot  is  reckoned  in 
square  feet,  the  unit  being  a  square  one 
foot  on  each  side.  In  the  laboratory,  area 
is  often  measured  in  square  centimeters 
(cm2),  the  unit  being  a  square  one  centi- 
meter on  each  side.  It  is  evident  from 
figure  4  that  one  square  inch  is  equal  to 
about  6  square  centimeters.  More  accu- 
rately, it  is  2.54  X  2.54,  or  6.45  square 
centimeters. 


1  Cm? 


1  Square  inch 


Fi|:z*g  0fRthe  Vquare 

inch  and  the  square 
centimeter. 


6 


INTRODUCTION:    WEIGHTS  AND  MEASURES 


The  usual  method  of  determining  area  is  by  calculation  from  the 
measured  linear  dimensions.  Thus  the  area  of  a  rectangle  or  parallelo- 
gram is  equal  to  the  base  times  the  altitude  (A  =b  Xh).  The  area  of  a 
triangle  is  equal  to  ^  the  base  times  the  altitude  (A  =  %bXh).  The 
area  of  a  circle  is  equal  to  3.14  times  the  square  of  the  radius  (A  =  -n-r2). 

9.  Units  of  volume  or  capacity.  The  unit  of  volume  that  is 
most  extensively  used  is  the  volume  of  a  cube  whose  edge  is 

of  unit  length.  Thus  the  volume  of 
a  freight  car  is  reckoned  in  cubic 
feet,  the  unit  being  a  cube  one  foot 
on  each  edge.  In  the  laboratory  we 
measure  the  capacity  of  a  flask  in 
cubic  centimeters  (cm3).  The  liter  is 
the  volume  of  a  cube  (Fig.  5)  which 
is  10  centimeters  (about  4  inches) 
on  each  edge.  The  liter  is  therefore 


Fig.  5.  A  liter  box,  which  is 
a  cube  10  centimeters  on 
each  side. 


equal  to  1000  cubic  cen^meters. 


UNITS  OF  VOLUME 

ENGLISH. 

1  cubic  foot  (cu.  ft.)  =  1728  cubic  inches  (cu.  in.) 
1  cubic  yard  (cu.  yd.)  =  27  cubic  feet 

1  gallon  (gal.)  =  4  quarts  (qt.)  =  231  cubic  inches 

METRIC. 

1  liter  (1.)  =  1000  cubic  centimeters  (cm?) 
1  cubic  meter  (m?)  =  1000  liters 
1  liter  =  1.06  quarts 

The  volume  of  a  regular  solid  is  best  determined  by  calculation  from 
the  measured  linear  dimensions.  Thus  to  get  the  volume  of  a  box,  we 
find  the  product,  length  by  width  by  depth.  In  the  case  of  a  cylindrical 
figure  we  compute  the  area  of  the  base  (Trr2)  and  multiply  by  the  height. 
For  measuring  liquids  we  use  a  graduated  vessel  of  metal  or  glass. 
Thus  in  the  English  system  we  have  gallon  and  quart  measures,  and 
for  small  quantities,  measures  marked  in  fluid  ounces  (sixteenths  of 
a  pint).  In  the  metric  system  we  have  flasks  (Fig.  6)  and  graduates 
(Fig.  9).  A  teaspoon  holds  about  5  cubic  centimeters. 


UNITS  OF   WEIGHT 


PROBLEMS 

(Give  answers  to  three  significant  figures*) 


t 


2 


How  many  centimeters  equal  1  foot  ?  4" 

How  many  inches  equal  76  centimeters  ? 

How  many  feet  equal  1  meter? 

A  boy  is  5  feet  6  inches   tall.     Express  his 
height  in  centimeters. 

6.   Express  1  kilometer  as  a  decimal  part  of  a  mile. 
(Remember  this  number.) 

6.  The  Falls  of  Niagara  on  the  American  side  are 
about  165  feet  high.     Express  this  in  meters. 

7.  The  diameter  of  a  certain  automobile  wheel 
with  its  tire  is  30  inches.      How  many  revolutions 
does   the  wheel  make  (a)  in  going  a  mile;  (6)  in 
going  a  kilometer  ?         v 

8.  An  aquarium  is  60  centimeters  long,  30  centi- 
meters wide,  and  45  centimeters  deep.     How  many 
liters  of  water  will  it  hold  ? 

9.  A  cylindrical  kerosene  can  holds  5  gallons.    If 
it  is  11  inches  in  diameter,  how  tall  must  it  be? 

10.  A  cylindrical  quart  measure  is  6  inches  high. 
What  is  its  diameter? 

11.  A  cylindrical  berry  box  is  measured  and  found  to  be  6.15  inches 
in  diameter  and  2.1  inches  deep.     What  is  its  capacity  in  dry  quarts? 
(In  the  United  States  a  dry  quart  is  67.2  cubic  inches.) 

12.  A  cylindrical  jar  is  4  inches  in  diameter  and  10  inches  deep. 
How  many  liters  will  it  hold  ? 

13.  A  water  tank  is  2  meters  long,  150  centimeters  wide,  and  80  cen- 
timeters deep.    How  many  gallons  will  it  hold? 


Fig.  6.  A  flask 
which  holds  i 
liter  when  filled 
to  the  mark  on 
the  neck. 


10.  Units  of  weight.f  The  kilogram  is  the  weight  of  a  certain 
platinum-iridium  cylinder  which  is  preserved  with  the  standard 
meter  near  Paris,  or  that  of  a  very  accurate  copy  of  this  cylinder 

*  For  an  explanation  of  what  is  meant  by  "  significant  figures  "  consult  your 
laboratory  manual. 

t  The  distinction  between  weight  and  mass  will  be  made  in  section  151. 


8 


INTRODUCTION:    WEIGHTS  AND  MEASURES 


which  is  deposited  in  the  United  States  Bureau  of  Standards  in 
Washington.  It  was  intended  that  each  of  these  cylinders 
should  weigh  the  same  as  one  liter  of  pure  water,  although  this 
has  turned  out  to  be  not  quite  true.  Yet  it  is  nearly  enough 
true  for  our  present  purposes.  Therefore  the  gram,  which  is 
the  one-thousandth  part  of  a  kilogram,  is  the  weight  of  one 
cubic  centimeter  of  water.  It  may  be  helpful  to  remember 
that  our  5-cent  nickel  piece  weighs  5  grams  and  our  silver  half- 
dollar  weighs  12.5  grams. 

In  the  United  States  the  pound  avoirdupois  is  defined  legally 


as 


2.204622 


ENGLISH. 


METRIC. 


of  a  kilogram. 

UNITS  OF  WEIGHT 

1  pound  (Ib.)  =  16  ounces  (oz.) 
1  ton  (T.)  =  2000  pounds 


1  gram  (g.)  =  1000  milligrams  (mg.) 
1  kilogram  (kg.)  =  1000  grams 
1  kilogram  =  2.20  pounds 
1  cubic  foot  of  water  weighs  62.4  pounds 
1  cubic  centimeter  of  water  weighs  1  gram 

11.  Weighing  machines.     The  spring  balance  (Fig.  7)  is  a 
simple  machine  for  getting  the  weight  of  things,  or  for  meas- 
^^  uring  forces  of  other  kinds,  such  as  the  pull 

exerted  by  a  rope.  It  contains  a  coiled 
spring,  and  the  force  exerted  is  indicated  by 
the  pointer  on  the  scale.  The  spring  balance  is 
very  extensively  used  because  of  its  great  con- 
venience, and  its  indications  are  close  enough 
for  many  practical  purposes. 
'^  The  platform  balance  (Fig.  8)  consists  of  a 

Fig.  7.    Spring    delicately  mounted  equal-arm  balance-beam  with 
balance.        a  pan  supported  at  each  end.     The  balance  is 


DENSITY 


used  to  show  the  equality  of  the  weights  of  two  bodies ;  that 
is,  two  things  are  said  to  have  the  same  weight  if  they  bal- 
ance each  other  when 
supported  on  the  ends 
of  an  equal-arm  bal- 
ance. The  determina- 
tion of  the  weight  of 
any  object  by  the 
platform  balance  de- 
pends upon  the  use  of 

a  set  of  weights,  which  p.g  g     Platform  balance. 

may  be  combined  in 
such  a  way  as  to  match  the  weight  of  the  object. 

PROBLEMS 

1.  How  many  grams  equal  1  pound? 

2.  How  many  grams  equal  1  ounce? 

3.  A  girl  weighs  52.5  kilograms.     Express  her  weight  in  pounds. 

4.  American  railways  usually  allow  each  passenger  150  pounds  of 
baggage.     Express  this  in  kilograms. 

6.  A  metric  ton  is  1000  kilograms.  How  many  pounds  is  this  in 
excess  of  the  English  ton? 

6.  It  is  sometimes  said,  "A  pint  is  a  pound,  the  world  around." 
How  many  pounds  does  a  pint  of  water  weigh?     (1  quart  =  2  pints.) 

7.  An  empty  milk  bottle  is  found  to  weigh  720  grams,  and  when 
it  is  filled  with  water,  the   bottle   and   water   weigh    1670  grams: 
(a)  how  many  cubic  centimeters  does  it  contain?      (6)   how  many 
liters?     (c)  how  many  quarts? 

8.  A  boy  5  feet  4  inches  tall,  and  weighing  140  pounds,  can  run  100 
yards  in  11  seconds.     Express  these  facts  in  metric  units. 

9.  If  sugar  sells  for  6  cents  a  pound,  how  much  would  1  metric  ton 
cost? 

10.  If  the  current  price  of  platinum  is  $75.00  per  ounce,  what  would 
be  the  price  per  gram  ? 

12.  Density.  Everyone  knows  that  lead  is  "  heavier  "  than 
cork ;  and  yet  the  question  is  sometimes  asked,  "  Which  is 
heavier,  a  pound  of  lead  or  two  pounds  of  cork?  "  The  word 


10         INTRODUCTION:    WEIGHTS  AND  MEASURES 

"  heavy  "  has  two  distinct  meanings.  Two  pounds  of  cork 
are  heavier  than  one  pound  of  lead  in  the  same  sense  that  two 
pounds  of  coal  are  heavier  than  one  pound  of  coal.  In  this 
case  the  word  "  heavy  "  refers  to  the  total  weight  of  the  mate- 
rial. On  the  other  hand,  lead  is  " heavier"  than  cork  in  the 
sense  that  a  piece  of  lead  weighs  more  than  an  equal  bulk  of 
cork.  The  word  "  density  "  is  used  to  designate  more  pre- 
cisely this  inherent  property  of  the  lead  and  the  cork.  That 
is,  lead  has  a  greater  density  than  cork. 

The  density  of  a  substance  is  its  weight  per  unit  volume. 
Thus  the  density  of  water  is  about  62.4  pounds  per  cubic  foot, 
or  8.34  pounds  per  gallon.  The  density  of  copper  is  555  pounds 
per  cubic  foot,  or  0.321  pounds  per  cubic  inch.  In  scientific 
work  it  is  usual  to  specify  the  density  of  a  substance  in  grams 
per  cubic  centimeter  (g/cm3)^. 

TABLE  OF  DENSITIES  * 
(In  grams  per  cubic  centimeter) 

Platinum 21.5  Hard  woods  (seasoned)    .  0.7-1.1 

Gold 19.3  Softwoods  (seasoned)  .    .0.4-0.7 

Mercury      .     .     .   *    .    .  13.6  Ice 0.911 

Lead 11.4  Human  body   .    .    .     .     .  0.9-1.1 

Silver 10.5  Cork 0.25 

Copper 8.93  Sulf uric  acid  (cone.)      .     .  1.84 

Brass       8.4  Sea  water 1.03 

Iron    .......  7.1-7.9  Milk 1.03 

Zinc 7.1  Fresh  water 1.00 

Glass 2.4-4.5  Kerosene 0.80 

Granite,  marble,  etc.   .  2.5-3.0  Gasoline  .     T 0.75 

Aluminum 2.65  Air about  0.0012 

13.  Measurement  of  density.  The  simplest  way  to  deter- 
mine the  density  of  a  substance  is  to  weigh  the  substance  and 
measure  its  volume.  • — -~ 

FOR  EXAMPLE,  a  piece  of  pine  6  feet  long,  1  foot  wide,  and  6  inches 
thick  has  a  volume  of  3  cubic  feet.  If  it  weighs  90  pounds,  its  density 
is  30  pounds  per  cubic  foot. 

*  This  table  is  for  reference  and  is  not  to  be  memorized. 


MEASUREMENT  OF  DENSITY  11 

An  empty  kerosene  can  weighs  1.25  pounds,  and  when  filled  with 
kerosene,  it  weighs  36.25  pounds,  so  that  the  net  weight  of  the  kero- 
sene in  the  can  is  35  pounds.     If  the  can  holds  5  gal- 
lons, the  density  of  the  kerosene  is  7  pounds  per  gallon. 

A  block  of  steel  is  15  centimeters  long,  6  centi- 
meters wide,  and  1.5  centimeters  thick  and  weighs 
1050  grams  ;  then  the  density  is  *£££  >  or  ^8  grams 
per  cubic  centimeter. 

To  find  the  density  of  an  irregular  piece  of  stone, 
we  may  determine  its  volume  by  the  displacement 
of  water.     Suppose  we   have  100  cubic  centimeters 
of  water  in  a  graduated  cylinder,  and  when  the  stone 
is  put  in,  the  water  level  rises  to  160  cubic  centi- 
meters (Fig.  9).     Then  the  volume  is  60  cubic  centi-     ated*  cylinder 
meters.      If  the  stone  weighs  150  grams,  its  density     used  to  find  vol- 
is  J^-,  or  2.5  grams  per  cubic  centimeter.  ume  of  stone. 


From  the  preceding  examples  it  will  be  seen  that  the  density 
of  a  body  is  found  by  dividing  its  weight  by  its  volume.    Thus, 

Density  = 


volume 

It  is  also  evident  that  if  we  know  the  density  of  a  substance, 
we  can  compute  the  weight  of  any  volume  "of  the  substance. 
By  this  method  engineers  calculate  the  weight  of  buildings  and 
bridges  which  it  would  be  impossible  to  weigh.  For, 

Weight  =  density  X  volume. 

FOR  EXAMPLE,  an  engineer  finds  by  computation  that  a  reenforced 
concrete  pier  contains  £500  cubic  feet  of  material,  and  he  knows  that 
such  material  averages  ISOjp^aun^s  per  cubic  foot.  Then  the  weight  of 
the  pier  is  equal  to  2500  times  150,  or  375,000  pounds  (about  188  tons). 

If  it  is  the  volume  of  a  thing  that  we  want  to  know,  we  have 

weight 


Volume  = 


density 


FOR  EXAMPLE,  the  volume  of  a  100-gram  brass  weight  is^^-,or  11.9 
cubic  centimeters. 


12         INTRODUCTION:    WEIGHTS  AND  MEASURES 

PROBLEMS 

(Use  data  given  in  table  on  page  10  when  necessary.) 

1.  A  block  of  iron  is  10  centimeters  by  8  centimeters  by  5  centi- 
meters, and  weighs  3  kilograms.     What  is  its  density  expressed  in 
grams  per  cubic  centimeter? 

2.  A  block  of  stone  measures  4  feet  by  2  feet  by  15  inches,  and 
weighs  1625  pounds.     Find  its  density  in  pounds  per  cubic  foot. 

3.  A  flask  with  a  capacity  of  120  cubic  centimeters  is  filled  with 
mercury.     How  many  kilograms  of  mercury  does  it  hold  ? 

4.  An  aluminum  cylinder  is  8  centimeters  long  and  4  centimeters 
in  diameter.     How  many  grams  does  it  weigh? 

6.  What  is  the  weight  of  a  granite  sphere  6  feet  in  diameter? 
Assume  the  density  of  granite  to  be  170  pounds  per  cubic  foot.  Vol- 
ume of  a  sphere  =  ^TrD3. 

6.  Given  the  density  of  water  in  the  English  system  as  62.4  pounds 
per  cubic  foot,  and  a  table  of  densities  in  the  metric  system,  how  would 
you  compute  the  corresponding  densities  in  the  English  system? 

7.  How  many  pounds  does  1  cubic  foot  of  aluminum  weigh  ? 

8.  The  cork  in  a  life  preserver  weighs  20  pounds.     What  is  its 
volume  in  cubic  feet? 

9.  A  cake  of  ice  measures  18  inches  by  12  inches  by  10  inches. 
How  many  pounds  does  it  weigh? 

10.  A  cylindrical  railway  water  tank  measures  on  the  inside  10  feet 
in  depth  and  6  feet  in  diameter.     How  many  tons  of  water  does  it 
hold? 

11.  A  quart  bottle  is  weighed  empty  and  then  full  of  milk.     How 
many  pounds  should  it  gain  in  weight  ? 

12.  A  silver  ball,  apparently  solid,  is  in  reality  hollow.     It  weighs 
4.5  kilograms  and  is  10  centimeters  in  diameter.     What  is  the  vol- 
ume of  the  cavity?  ~* 

13.  A  metal  tube  weighs   10.1   kilograms.     It  is   10  centimeters 
long,  its  outside  diameter  is  13  centimeters,  and  its  inside  diameter 
is  5  centimeters.     Find  (a)  the  density  of  the  metal  and  (6)  what 
the  metal  probably  is. 

14.  How  many   cubic   centimeters   of   concentrated   sulfuric   acid 
must  be  added  to  1  liter  of  water  in  order  that  the  diluted  acid  may 
have  a  density  of  1.3  grams  per  cubic  centimeter? 

16.   Calculate  the  volume  in  cubic  feet  of  your  own  body. 


13 


14.  Units  of  time.  The  secon<3Wthe  minute,  and  the  hour 
are  used  by  all  civilized  nations  as^nits  of 
time.  An  hour  is  one  twenty-fourthVf  the 
time  from  noon  to  noon.  A  minute  is  a 
sixtieth  of  an  hour ;  and  a  second  is  a  six- 
tieth of  a  minute.  Thus  an  hour  contains 
60  times  60,  or  3600  seconds,  and  a  mean  solar 
day  contains  24  X  3600,  or  86,400  seconds. 

Ordinary  time  intervals  are  measured  with 
clocks  or  watches.      For  short   intervals   a 
special  type  of  watch  is  used,  known  as  a  Fig-   10. 
stop  watch   (Fig.   10) ;  it  can  be  read  to  a 

fifth  of  a  second.  fifth  of  a  second. 


A    stop 


SUMMARY  OF  PRINCIPLES  IN  CHAPTER  I 

Density  is  weight  of  unit  volume. 

weight 

Density  =— 7-^ — 
volume 

Weight  =  density  X  volume. 

__  ,  weight 

Volume  =  - — —. — 
density 

QUESTIONS* 

1.  What  are  the  meanings  of  the  prefixes  kilo-,  centi-,  and  milli-, 
used  in  the  metric  system?  - 

2.  What  two  uses  has  cork  which  depend  on  its  small  density ;  and 
what  three  uses  has  lead  due  to  its  great  density  ? 

3.  How  would  you  measure  the  diameter  of  a  small  steel  ball? 

4.  How  can  the  thickness  of  this  page  be  measured  ? 

*  In  trying  to  find  the  answers  to  these  questions,  the  student  is  expected  to 
consult  various  reference  books,  such  as  dictionaries,  encyclopedias,  engineering 
handbooks,  and  popular-science  magazines.  He  is  also  expected  to  keep  his 
eyes  open  outside  of  the  classroom,  and  to  ask  questions  of  artisans  and  business 


14         INTRODUCTION:    WEIGHTS  AND  MEASURES 

6.   What  is  the  difference  between  a  ship's  chronometer  and  an  alarm 
clock? 

6.  How  could  you  determine  the  inside  diameter  of  a  glass  tube 
which  has  a  fine  bore? 

7.  Read  in  an  encyclopedia  the  history  of  our  English  standards  of 
length. 

8.  Learn  from  an  encyclopedia  about  the  origin  of  the  metric  sys- 
tem.    When  was  it  officially  introduced  into  the  United  States  ? 

9.  What  advantages  has  the  metric  system  over  the  English  sys- 
tem of  measures? 

10.   Why  is  it  that  the  United  States  and  Great  Britain  are  the  only 
two  civilized  countries  that  do  not  use  the  metric  system  commercially? 

PRACTICAL  EXERCISES 

1.  Standard  time.     How  does  your  local  jeweler  get  "standard 
time,"  by  which  to  set  his  clocks  and  watches  correctly? 

2.  Errors  of  measures.     How  would  you  test  the  accuracy  of  a 
quart  measure?     Bring  one  from  home  and  try  it. 

3.  Household  measurements.    What  units  of  measurement  are  used 
in  your  home?     Make  a  list  of  all  units  found,  and  show  how  they  are 
related.     (Consult  Measurements  for  the  Household.  —  U.  S.  Bureau  of 
Standards  Circular  No.  55.) 

4.  Accuracy  of  a  storekeeper.     How  nearly  right  must  a  quart  meas- 
ure be  to  be  legally  permissible  for  a  storekeeper  to  use  in  your  state  ? 
How  nearly  right  must  a  storekeeper's  scales  be  to  be  legally  permis- 
sible?    (Hint.     Make  an  excursion  to  your  City  Sealer's  office.) 

5.  Accuracy  of  a  carpenter.     When  a  house  is  built,  what  errors  in 
distances  are  considered  allowable  in  setting  up  the  frame  as  compared 
with  what  the  plans  call  for  ? 

6.  Accuracy  of  a  machinist.     Automobile  cylinders  often  wear  more 
on  one  side  than  on  another  so  that  they  become  oval  instead  of  round. 
When  testing  for  this,  how  closely  does  an  automobile  repair  man  meas- 
ure various  diameters  of  a  cylinder? 


CHAPTER  II 
SIMPLE  MACHINES 

Levers  of  various  kinds  —  principle  of  moments  —  force  at 
the  fulcrum  —  center  of  gravity  in  general  —  weight  of  a 
lever  —  stability  —  mechanical  advantage  —  wheel  and  axle 
—  pulley  systems  —  parallel  forces. 

Work  —  principle  of  work  —  differential  pulley  —  inclined 
plane  —  wedges  and  cams  —  screws  —  gears  —  combinations 
of  sirnple  machines  —  power  —  transmission  of  power. 

Friction  —  traction  —  factors  affecting  friction  —  lubri- 
cation —  coefficient  of  friction  —  efficiency  of  machines. 

15.  Why  we  use  machines.  With  a  rope  and  tackle  a  man 
can  lift  a  piano  up  to  a  window  on  the  second  floor.  With  a 
skid  a  boy  can  roll  a  barrel  of  flour  up  into  a  truck.  With  a 
claw  hammer  a  girl  can  pull  a  nail  out  of  a  box,  although  she 
could  not  move  the  nail  at  all  with  her  fingers  alone.  It  is 
obvious  that  we  can  do  many  things  with  the  aid  of  simple 
machines  that  otherwise  would  be  quite  impossible  because  we 
are  not  strong  enough.  In  other  words,  machines  enable  us 
to  multiply  the  force,  that  is,  the  push  or  pull,  which  we  can 
exert.  Furthermore,  some  machines  help  us  to  do  things  more 
quickly  or  more  conveniently  than  we  could  without  them. 
For  example,  with  a  fishing  rod  we  can  place  the  bait  to  better 
advantage  and  can  haul  in  the  fish  much  faster.  Most  im- 
portant of  all,  we  often  employ  machines  in  order  to  make  use 
of  forces  exerted  by  animals,  wind,  water,  or  steam. 

In  this  chapter  we  shall  learn  that  all  complex  machines  are 
built  out  of  simpler  parts  —  levers,  wheels,  cranks,  gears, 
pulleys,  etc.  We  shall  learn  to  compute  how  much  advantage 
we  gain  by  the  use  of  various  complex  machines  and  how  to 
use  them  more  efficiently. 

15 


16 


SIMPLE  MACHINES 


16.  A  lever  with  two  equal  weights.     Doubtless  the  simplest 
machine  is  a  lever,  such  as  a  seesaw  or  the  scale  beam  of  a 

platform  balance  or  the  walking  beam 
of  a  steamboat.  In  the  case  of  the 
balance  (Fig.  11),  the  beam  swings 
freely  under  the  influence  of  the  equal 
weights  W\  and  Wz  only  when  the 
distance  AF  equals  the  distance  BF. 
In  general,  equal  weights  mil  balance 
only  when  placed  at  equal  distances 
from  the  point  of  support.  In  the 
technical  language  of  physics,  this 
point  F  about  which  the  rigid  bar 
turns  is  called  the  fulcrum.  The 
fulcrum  in  a  beam  balance  consists  of 
a  sharp  hard  support  called  a  knife- 


fig,  ii.     A  lever  with  equal 
arms  and  equal  weights. 


edge,  and  each  end  of  the  beam  carries  a  pan  which  is  sus- 
pended from  a  knife-edge.  These  precautions  are  taken  to 
minimize  friction. 

17.  A  lever  with  two  unequal  weights.  Very  often  the 
weights  or  forces  applied  to  a  lever  are  not  equal;  as,  for  example, 
when  two  persons  of  un- 


equal  weight  are  seesawing,           p  —   —  dr  ^—d2-^. 

ftr  in  thp  na,sp  nf  fl.n  ordinary      1        1        |       |       |      • 

1     1 

pump  handle.    It  is  evident 
that  at  equal  distances  the          A 

Pi  \V 

larger  weight  would  have         so  g.  1 
the  greater  tendency  to  tip                             J^ 
the  lever.    It  is  also  evident 
that  with  equal  weights  at  Fig*  12'    Alever  ^ 

0^2 

100  g. 

> 

two  unequal  weights 

unequal  distances  the  weight  at  the  greater  distance  from  the 
fulcrum  has  the  greater  tendency  to  tip  the  lever.  There- 
fore in  order  to  have  two  unequal  weights  balance,  they  must 
be  so  placed  that  the  smaller  weight  is  at  the  greater  distance 
from  the  fulcrum. 


A  LEVER   WITH   THE  FULCRUM  AT  ONE  END       17 

If  we  balance  an  ordinary  meter  stick  in  the  middle  (Fig.  12)  and 
suspend  a  50-gram  weight  W\  at  A,  which  is  40  centimeters  from  the 
fulcrum  F,  and  then  hang  a  100-gram  weight  W2  on  the  other  side  at 
such  a  point  as  just  to  balance  the  first  weight,  we  shall  find  that  the 
point  B,  where  the  100-gram  weight  is  hung,  is  about  20  centimeters 
from  F,  or  half  as  far  from  the  fulcrum  as  the  50-gram  weight. 

Careful  experiments  show  that  any  two  unequal  forces  will 
balance  only  if  the  force  on  one  side  multiplied  by  its  perpen- 
dicular distance  from  the  fulcrum  equals  the  force  on  the  other 
side  multiplied  by  its  distance  from  the  fulcrum.  Thus,  in  fig- 
ure 12, 

Wi  X  di  =  W2  X  d2. 

This  relation  of  the  forces  and  distances  may  also  be  ex- 
pressed by  the  equation 


Fulcrum 


Effort 


Resistance 

Fig.  13.    Pliers  are  levers 
with  rivet  as  fulcrum. 


which  may  be  stated  in  words  as  follows :  the  forces  are  inversely 
proportional  to  their  distances  from_Jhe  fulcrum.  This  means 
that  if  one  force  is  three  times  as  great 
as  another,  then  it  must  be  one  third  as 
far  away  from  the  fulcrum  as  the  other 
in  order  to  make  the  lever  balance. 

Crowbars,  shears,  glove  stretchers, 
pliers  (Fig.  13),  etc.,  are  all  examples 
of  this  sort  of  lever. 

18.   A  lever  with  the  fulcrum  at  one  end.     When  a  wheel- 
barrow is  used  to  carry  a  heavy  weight  (Fig.  14),    we  have 

a  lever  with  the  fulcrum  F.  located 
at  one  end.  The  same  principle 
is  involved  as  in  the  levers  just 
discussed.  There  are  two  tenden- 
cies at  work  which  must  balance ; 
namely,  the  tendency  of  the  weight 
W  to  tip  the  lever  down  and  the 
the  wheel.  tendency  of  the  effort  E  or  pull 


18 


SIMPLE   MACHINES 


applied  to  lift  it  up.     The  weight  multiplied  by  the  perpen- 
dicular distance  from  the  fulcrum  to  its  line  of  action  measures 

its  turning  effect  about 
the  fulcrum ;  that  is,  its 
tendency  to  tip  the  lever 
down.  This  must  'be 
balanced  by  an  equal 
turning  effect  in  the  op- 
posite direction,  namely, 
the  effort  or  upward  pull 
multiplied  by  its  dis- 


201 


Fig.  15.     A  lever  with  fulcrum  F  at  one  end. 


tance    from     the     ful- 


crum. 


Suppose  we  fasten  a  light  stick  (Fig.  15)  by  an  axle  F  to  an  upright 
support  so  that  the  stick  is  free  to  turn,  and  hang  a  weight  /£,  say  20 
pounds,  at  a  distance  of  6  inches  from  the  fulcrum  F.  Then  if  we  pull 
up  with  a  spring  balance  at  a  point  B,  12  inches  from  the  fulcrum  F,  we 
find  that  the  effort  or  pull  E,  measured  by  the  spring  balance,  is  about 
10  pounds.  (Of  course  allowance  has  to  be  made  for  the  weight  of  the 
stick.) 

The  equation  representing  these  tendencies  to  turn  the  stick 
in  opposite  directions  would  be  as  before 

R  X  AF  =  E  X  BF. 

A  nutcracker  and  a  crowbar  .when  used  with  one  end  on 
the  ground  (Fig.  16)  are  examples  of  levers  with  the  fulcrum 
at  one  end. 

Sometimes,  as  in  the  case 
of  the  forearm  when  the 
hand  supports  a  weight,  the 
fulcrum  is  at  one  end  of 
the  lever,  the  weight  or  re- 
sistance to  be  overcome  is 

at  the   Other  end,    and  the   Fig.  16.     A  crowbar  used  with  the  ground 

effort   is   applied   at  some 


as  fulcrum. 


A  LEVER   WITH   THE  FULCRUM  AT  ONE  END       19 


point  in  between.  This  is 
further  illustrated  in  fig- 
ure 17  where  a  man  is 
shown  holding  a  weight  R 
on  a  shovel,  with  his  left 
hand  F  acting  as  the  ful- 
crum, while  he  applies 
an  upward  force  E  with 
his  right  hand. 

We  may  illustrate  this 
case  by  the  same  apparatus 
(Fig.  18)  which  we  have  just 
used.  In  this  experiment  we 
place  the  10-pound  weight 
R  12  inches  from  the  ful- 
crum F  and  attach  the 
spring  balance  E  at  a  point 
6  inches  from  the  fulcrum. 
We  find  that  the  pull  needed 
is  now  20  pounds,  or  just 

double  the  weight.    In  this  case  the  weight-distance  is  double  the 
effort-distance,  and  the  effort  is  double  the  weight. 


Fig.  17.  The  shovel  is  a  lever  with  weight 
near  one  end;  hand  at  other  end  acts  as 
fulcrum. 


Fig.  1 8.     A  lever  with  weight  at  one  end  and  fulcrum  at  the  other  end. 

Thus  we  see  that  the  same  principle  holds  wherever  the 
resistance  (weight)  and  the  effort  (upward  pull)  are  applied. 
This  may  be  stated  as  follows : 

Resistance  X  its  distance  from  fulcrum 
=  effort  X  its  distance  from  fulcrum. 


20 


SIMPLE  MACHINES 


Fig.  19.     Wheelbarrow  with  two  weights. 


19.  Lever  with  two  weights.    It  often  happens  that  a  wheel- 
barrow is  used  to  carry  two  weights,  such  as  two  bags  of  cement 

or  a  box  and  a  keg, 

jp  I ^  ^M  as  shown  in  figure 

'"  I'  19.    To  get  the  up- 

ward pull  we  have 
merely  to  compute 
the  turning  effect  of 
each  of  the  weights 
W  i  and  W 2  about 
the  fulcrum  F  and  make  the  sum  of  these  effects  equal  to  the 
turning  effect  of  the  upward  pull  or  effort  E.  That  is, 

Wi  X  BF  +  Wz  X  AF  =  E  X  CF. 

The  distances  CF,  BF,  and  AF  should  be  measured  perpendicularly  to  the 
lines  of  action  of  the  forces. 

In  general,  then,  we  see  that  we  can  balance  the  turning 
effect  of  two  or  more  weights  by  multiplying  each  weight  by 
the  perpendicular  distance  of  its  line  of  action  from  the  fulcrum, 
and  making  the  sum  of  these  products  equal  to  the  product 
of  the  effort  by  the  perpendicular  dis- 
tance of  its  line  of  action  from  the 
fulcrum. 

20.  Principle  of  moments.    It  has  been 
seen  that  the  turning  effect  of  a  force 
depends  on  two  factors,  the  amount  of 
the  force  and  the  distance  of  its  line  of 
action  from  the  fulcrum.    This  product  — 
force    times   its    perpendicular    distance 
from  the  fulcrum  —  is  called  the  moment 
of  the  force. 


Fig.  20.  Moment  of  a 
force  equals  force  times 
its  perpendicular  dis- 
tance from  fulcrum. 


For  example,  let  AF  (Fig.  20)  be  a  rigid  bar  which  can  rotate 
about  F.  The  moment  of  the  force  B  applied  at  A  is  equal  to  B  4jmes 
FA ;  and  the  moment  of  force  C  is  equal  to  C  times  FD.  If  B  equals 
C,  which  is  the  greater  moment  ? 


FORCE  AT   THE  FULCRUM  21 

In  general,  for  a  lever  to  be  in  equilibrium,  the  sum  of  the 
moments  of  the  forces  tending  to  turn  it  in  one  direction  must 
equal  the  sum  of  the  moments  of  the  forces  tending  to  turn  it  in 
the  opposite  direction. 

QUESTION 

A  mechanic  finds  difficulty  in  turning  an  inch-pipe  with  a  6-inch 
Stillson  wrench  but  finds  it  easy  to  turn  the  pipe  with  an  18-inch 
wrench.  Explain. 

21.  Force  at  the  fulcrum.  In  the  case  of  the  man  with  the 
shovel  (Fig.  17),  we  have  called  his  left  hand  the  fulcrum.  But 
it  is  quite  as  evident  that  this  hand  must  exert  a  force  (in  this 
case  a  downward  push)  as  that  the  other  hand  must  pull  up. 
Indeed,  we  might  have  thought  of  the  right  hand  as  the  ful- 
crum of  a  lever  with  unequal  arms  and  the  left  hand  as  exert- 
ing the  effort. 

In  general,  when  three  forces  act  on  any  object,  the  point  of 
application  of  any  one  of  the  three  forces  can  be  thought  of  as  the 
fulcrum,  and  the  other  two  forces  as  resistance  and  effort  respectively. 

Seesaw  Wheelbarrow  Shovel  General  case 

F  E  F  E  A 


I t t    __L 


I         J  I 


R  R  F     B  C 

F=R+E  R=E+F  E=R+F  A=B+C 

Fig.  21.     Force  exerted  at  the  fulcrum  of  a  lever. 

To  find  how  much  force  the  fulcrum  exerts  in  any  of  the  cases 
so  far  discussed,  we  may  draw  diagrams  like  those  in  figure  21. 
In  the  first  diagram  the  fulcrum  is  between  the  weights  or 
forces,  as  in  the  case  of  a  seesaw;  in  the  next  diagram  the 
fulcrum  is  at  one  end  and  the  effort  at  the  other,  as  in  the  ease 
of  a  wheelbarrow ;  in  the  third  diagram  the  fulcrum  and 
resistance  are  at  the  ends,  as  in  the  case  of  a  shovel.  In  all 
cases  the  principle  is  exactly  the  same  (see  general  case). 


22  SIMPLE  MACHINES 

When  there  are  three  (or  more)  parallel  forces  in  equilib- 
rium, the  sum  of  the  forces  pulling  one  way  must  equal  the  sum 
of  the  forces  pulling  the  other  way.  By  applying  this  principle 
in  any  particular  case,  we  get  an  equation,  like  one  of  those  in 
figure  21,  which  can  be  solved  for  F,  the  force  exerted  by  the 
fulcrum. 

QUESTIONS  AND  PROBLEMS 

(Make  diagrams  to  illustrate  the  following  problems.) 

1.  Draw  an  outline  sketch  and  indicate  the  fulcrum  and  the  direc- 
tion of  the  two  forces  in  the  case  of  a  pair  of  shears,  a  glove  stretcher,  a 
can  opener,  a  pair  of  tongs,  and  a  nutcracker,  regarded  as  examples  of 
the  lever. 

2.  What  weight  placed  20  inches  from  the  fulcrum  will  balance  100 
pounds  placed  8  inches  away  on  the  opposite  side  ?     What  is  the  force 
exerted  at  the  fulcrum  ? 

*"3.  A  piece  of  wire  which  is  to  be  cut  with  shears  is  placed  0.5  inches 
from  the  rivet.  If  a  force  of  25  pounds  is  applied  on  the  handles  6 
inches  from  the  rivet,  how  much  force  is  exerted  on  the  wire  ? 

4.  Why  are  the  shears  used  for  cutting  paper  made  with  long  blades 
and  short  handles,  while  those  used  to  cut  metal  are  just  the  opposite  ? 

6.  A  plank  12  feet  long  is  to  be  used  as  a  seesaw  by  two  boys  who 
weigh  100  pounds  and  140  pounds.  How  far  from  the  lighter  boy  must 
the  prop  be  placed  ?  (Let  x  =  distance  from  small  boy  and  12  —  x  = 
distance  from  big  boy.  Neglect  weight  of  plank.) 

6.  The  handles  of  a  wheelbarrow  (Fig.  14)  are  4  feet  6  inches  from 
the  axle,  and  the  load  of  200  pounds  can  be  considered  as  18  inches  from 
the  axle.     How  much  effort  must  be  exerted  to  raise  the  handles  ? 

7.  Why  is  it  easier  to  lift  the  handles  of  a  wheelbarrow  if  the  load  is 
placed  as  near  the  wheel  as  possible? 

8.  In  lifting  a  shovel  full  of  coal  do  you  lift  up  with  one  hand  as  hard 
as  you  push  down  with  the  other?    Explain. 

9.  When  a  load  is  carried  on  a  stick  over  the  shoulder,  why  should 
the  load  be  carried  near  the  shoulder  rather  than  far  out  on  the  stick  ? 

10.  A  crowbar  5  feet  6  inches  long  is  used  to  lift  a  weight  of  400 
pounds.     The  fulcrum  is  placed  6  inches  from  the  weight.     Calculate 
the  effo/t  needed.     (Two  solutions  are  possible.) 

11.  What  levers  are  there  in  the  human  body  ? 


CENTER  OF  GRAVITY 


23 


22.  Center  of  gravity.     So  far  in  our  study  of  levers  we  have 
assumed  that  the  weight  of  the  lever  itself  could  be  neglected, 
but  in  practice  this  is  not  always  the  case.     It  is  our  problem 
now  to  find  how  to  make  allowance  for  the  weight  of  the  lever. 

We  have  already  seen  that  a  lever  carrying  two  weights 
(Fig.  22)  can  be  supported  at  a  point  in  between,  which  we  have 
called  the  fulcrum, 
but  which  we  may 
now  call  the  "  center 
of  gravity  "or  "cen- 
ter of  weight." 
The  force  neces- 
sary to  support  this 
point  is  the  same 
as  it  would  be  if 
the  whole  weight 

were     concentrated  Fig*22'     Center  of  gravity  of  two  weights. 

there.  In  the  same  way  we  could  support  a  bar  carrying 
three  or  more  weights  on  a  single  fulcrum,  if  it  is  placed  at 
the  right  point.  That  point  would  be  the  center  of  gravity  of 
the  weights.  In  general,  the  center  of  gravity  of  a  body  is 
the  point  at  which  we  can  consider  its  whole  weight  concentrated. 
To  find  the  position  of  the  center  of  gravity,  we  have  simply 
to  find  the  point  at  which  the  object  would  balance  on  a 
knife-edge.  This  may  be  computed,  but  it  is  usually  easier 
to  locate  it  experimentally. 

23.  How  to  find  a  center  of  gravity  by  experiment.     If  the 
shape  of  the  object  is  simple  and  its  density  is  everywhere  the 
same,  as  in  the  case  of  a  shaft  or  a  board,  we  should  expect 
the  center  of  gravity  to  be  in  the  middle,  and  if  we  try  to  balance 
the  object  on  some  sharp  edge,  we  find  that  the  center  of  gravity 
is  indeed  located  at  the  geometrical  center.     In  the  case  of 
an  irregularly  shaped  object  like  a  baseball  bat,  the  simplest 
way  is  to  balance  the  bat  on  a  knife-edge.     In  the  case  of  a 
chair,  the  center  of  gravity  may  be  found  by  considering  that,  if 


24 


SIMPLE  MACHINES 


the  chair  is  hung  so  as  to  swing  freely,  the  center  of  gravity 
will  lie  directly  under  the  point  of  suspension.  Therefore,  if 
a  chair  or  any  other  irregular  object  is  hung  from  two  points 

successively,  the  point  of  intersec- 
tion of  the  plumb  lines  from  these 
points  will  locate  the  center  of 
gravity. 


Fig.  23.     Finding  the  center  of 
gravity  with  a  plumb  line. 


To  make  this  clear,  let  us  take  an 
irregular  sheet  of  zinc  and  drill  three 
holes  near  the  edge,  A,  B,  and  C  in 
figure  23.  Let  the  zinc  be  hung  from 
a  pin  put  through  the  hole  A,  and  let 
a  plumb  line  also  be  hung  from  the  pin. 
Draw  a  line  on  the  zinc  to  show  where 
the  plumb  line  crosses  it.  Then  let  the 
zinc  be  hung  from  another  hole  B  and  draw  another  line  in  a  similar 
way.  The  point  of  intersection  G  is  the  center  of  gravity.  When  the 
zinc  is  hung  from  the  third  hole  C,  the  plumb  line  will  pass  through 
the  center  of  gravity  already  found. 

In  the  case  of  a  ring,  or  a  cup,  or  a  boat,  the  center  of  gravity 
will  not  lie  in  the  substance  itself,  but  in  the  empty  space  inside ; 
but    this    will    not    bother    us    in 
answering  questions  about  how  such 
objects  act.     We  may,  if  we  like, 
think  of  such  a  center  of  gravity  as 
rigidly  attached  to  the  object  by  a 
very  light,  stiff  framework. 

We  shall  find  this  idea  of  the 
center  of  gravity  especially  conven- 
ient in  problems  where  the  weight 
of  a  lever  has  to  be  considered,  for 
we  can  now  assume  that  the  whole  weight  of  the  lever  is  con- 
centrated and  acting  at  its  center  of  gravity. 

FOR  EXAMPLE,  suppose  an  18-ounce  hammer  balances  10  inches  from 
the  handle  end.  When  a  fish  is  tied  to  the  end  of  the  handle,  the  whole 
balances  6  inches  from  the  end.  How  much  does  the  fish  weigh? 


Fig.    24.     Balancing    a   fish 
against  the  weight  of  a  hammer. 


STABILITY 


25 


Let  us  first  draw  a  careful  diagram  (Fig.  24).  We  may  consider 
the  weight  of  the  hammer,  18  ounces,  as  concentrated  at  a  point  CG,  10 
inches  from  the  end  of  the  handle  or  4  inches  from  the  fulcrum.  Let  x 
be  the  weight  of  the  fish,  which  is  applied  6  inches  from  the  fulcrum. 
Then  we  have 

6  z  =  4  X  18 

x  =  12  ounces,  the  weight  of  the  fish. 

24.  Stability.  The  conception  of  center  of  gravity  also  helps 
us  to  understand  another  kind  of  problem. 

If  we  place  a  block  A  on  an  inclined  plane  and  drop  a  plumb  line  from 
its  center  of  gravity,  the  line  falls  within  the  base  of  the  block  (Fig.  25). 
If  we  place  on  the  same  inclined 
plane  another  block  B  which  has 

the   same  base  but   twice   the  /     ^s.  /  /  \ 

height  of  A,  a  plumb  line  from  /  „„       /  /  /     *i 

its  center  of  gravity  will  fall 
outside  the  base  and  the  block 
B  will  tip  over. 

In  general,  an  object  will 
be  stable,  that  is,  it  will  not 
tip  over  of  itself,  if  a  plumb 

line  from  its  center  of  gravity  Fi8-  25-  Stable  and  unstable  objects, 
falls  within  its  base.  This  is  called  the  condition  of  stability. 
Some  objects  are,  however,  easier  to  knock  over  than  others, 
even  though  they  will  not  tip  over  of  themselves.  Evidently 
the  stability  of  an  object  in  this  sense  is  greater,  the  greater 
its  weight,  the  larger  its  base,  and  the  lower  its  center  of  gravity. 

QUESTIONS  AND  PROBLEMS 

1.  A  uniform  bar  10  feet  long  has  a  load  of  45  pounds  suspended 
from  one  end  and  balances  when  a  support  is  placed  2  feet  from  that 
end.     What  is  the  weight  of  the  bar?     (The  center  of  gravity  of  the 
bar  is  in  the  middle.) 

2.  The  standard  length  of  a  railroad  rail  is  33  feet,  and  a  size  com- 
monly used  weighs  80  pounds  per  yard.     If  four  men  take  hold  of  one 
end  of  such  a  rail  lying  on  the  ground,  how  much  must  each  man  lift  in 
order  to  raise  the  end  from  the  ground  ? 


26 


SIMPLE  MACHINES 


3.  A  boy  has  a  2-pound  fishing  rod  10  feet  long,  the  center  of  gravity 
of  which  is  3.5  feet  from  the  thick  end.     He  finds  the  weight  of  his 
string  of  fish  by  hanging  them  from  the  thick  end  of  the  rod  and  then 
balancing  the  rod  on  a  fence  rail.     He  notes  that  it  balances  at  a  point 
15  inches  from  the  end.     How  many  pounds  of  fish  has  he  ? 

4.  A  pole  20  feet  long  weighs  120  pounds.   When  a  30-pound  bag  of 
meal  is  hung  at  one  end,  the  balancing  point  is  3  feet  from  the  same 
end.     Where  is  the  center  of  gravity  of  the  pole  ? 

6.  A  6-foot  crowbar  balances  at  a  point  2.5  feet 
from  its  sharp  end.     If  a  weight  of  30  pounds  is 
hung  0.5  feet  from  this  end,  and  50  pounds  is  hung 
1  foot  from  the  other  end,  it  balances  at  its  mid- 
point.    How  heavy  is  the  bar  ? 

*^G.  A  uniform  beam  AB,  20  feet  long,  weighing 
600  pounds,  is  supported  by  props  placed  under  its 
ends.  Four  feet  from  prop  A  a  weight  of  200  pounds 
is  suspended.  Find  the  pressure  on  each  prop. 
(Regard  as  a  lever  with  its  fulcrum  at  one  end.) 

7.  A  man  and  a  small  boy  are  carrying  a  basket 
containing  a  load  of  100  pounds  by  means  of  a 
uniform  rod  10  feet  long.     If  the  weight  of  the  rod 
is  20  pounds,  where  must  the  basket  be  placed  so 
that  the  man's  load  will  be  three  times  that  of  the 
boy's? 


Fig.  26.     Leaning 
Tower  of  Pisa,  Italy. 


8.  Explain  why  the  Leaning  Tower  of  Pisa  (Fig.  26)  does  not  fall. 

9.  What  means  have  been  employed  to  increase  the  stability  of 
automobiles  ? 

10.  Explain  why  a  cart  loaded  with  hay  is  more  likely  to  overturn 
on  a  sidehill  than  the  same  cart  loaded  with  sand. 

11.  Explain  how  a  tip-cart  loaded  with  bricks  is  dumped  by  lifting 
up  the  front  edge  of  the  body 

a  few  inches  as  shown  in  fig- 
ure 27. 

12.  Compare    the   stability 
of  human  beings  with  that  of 
four-footed  animals. 

13.  Why  does  a  man  carry- 
ing a  trunk   upstairs    on   his  Fig.  2?.     shifting  the  center  of  gravity  ot 
back  bend  forward?     ,  the  load  by  tilting  the  cart  body. 


MECHANICAL  ADVANTAGE 


27 


14.  Illustrate  with  sketches  the  various  methods  employed  to  give 
the  proper  stability  to  objects  in  everyday  use,  such  as  lamps,  clocks, 
chairs,  pitchers,  vases,  etc. 

25.  Mechanical  advantage.  We  have  already  seen  that  a 
man  with  a  lever  may  lift  a  weight  of  500  pounds  by  exerting 
a  force  of  100  pounds.  In  this  case  the  resistance  that  can  be 
overcome  is  5  times  the  effort.  For  any  machine  the  ratio  of 
the  resistance  to  the  effort  is  called  the  mechanical  advantage. 

But  we  have  also  seen  that  the  resistance  is  to  the  effort 
inversely  as  the  relative  distances  of  the  resistance  and  effort 
from  the  fulcrum.  Often  it  is  more  convenient  to  compute 
the  mechanical  advantage  of  a  lever  by  dividing  the  lever  arm  of 
the  effort  by  the  lever  arm  of  the  resistance.  These  statements 
can  be  briefly  expressed  in  the  equation : 

resistance          effort  arm 


Mech.  adv.  = 


effort 


resistance  arm 


FOR  EXAMPLE,  the  arms  of  the  handle  of  an  ordinary  lift  pump  are  5 
inches  and  28  inches.  Then  the  mechanical  advantage  of  the  pump 
handle  is  -^-,  or  5.6.  This  means  that  1  pound  effort  exerted  on  the 
handle  gives  5.6  pounds  pull  on  the  pump  rod. 

26.  Bent  lever.  In  working  with  actual  levers  as  we  see 
them  in  practical  machines  we  often  find  that  the  lever  itself  is 
not  a  straight  bar,  but  is  bent  so  that  the 
two  arms  do  not  form  a  straight  line. 

FOR  EXAMPLE,  let  us  consider  the  case  of  an 
ordinary  claw  hammer  as  used  to  pull  out  a  nail 
(Fig.  28).  If  we  exert  at  B  a  pull  or  effort  E  of 
60  pounds,  what  is  the  resistance  R  which  the 
nail  offers?  We  must  first  measure  the  effort- 
arm  FB,  which  is  found  to  be  12  inches,  and 
then  the  resistance-arm  FA,  which  is  1.5  inches. 
Then  the  moment  of  the  effort  is  E  X  FB  and  the 
moment  of  the  resistance  is  R  X  FA.  Making 
these  two  moments  equal,  we  have 


60  X  12  =  #  X  1.5 
and  R    =  480  pounds. 


Fig.   28.     Claw  ham- 
mer acts  as  bent  lever. 


28 


SIMPLE  MACHINES 


In  this  case  it  will  be  seen  that  the  two  arms  of  the  lever  are 
inclined  to  each  other,  but  the  principle  of  moments  applies 
just  as  it  would  if  it  were  a  straight  lever.  We  shall  find  many 

examples  of  bent  levers  as  parts  of 
machines,  such  as  the  lever  used  in 
operating  the  brake  of  an  automo- 
bile, or  the  " bell-crank"  lever  used 
to  transmit  a  pull  around  a  corner 
in  a  railroad  signal  system.  We 
may  also  regard  many  other  objects, 
such  as  a  door  or  gate,  as  bent 
levers. 


Fig.  29. 


A   gate   regarded  as  a 
bent  lever. 


FOB  EXAMPLE,  suppose  a  gate  (Fig.  29)  3.5  feet  high  and  5  feet  wide 
weighing  100  pounds  swings  on  hinges  placed  3  inches  from  the  top  and 
3  inches  from  the  bottom,  (a)  What  is  the  vertical  force  exerted  by 
each  hinge  ?  (6)  How  great  is  the  horizontal  pull  exerted  by  the  upper 
hinge  ?  (c)  How  great  is  the  horizontal  push  exerted  by  the  lower  hinge  ? 

(a)  We  shall  assume  that  the  gate  is  properly  hung  and  that  the 
weight,  100  pounds,  is  equally  divided  between  the  two  hinges  ;  that  is, 
each  hinge  supports  50  pounds.     Therefore  the  vertical  forces  YI  and 
F2  are  each  equal  to  50  pounds. 

(b)  Let  us  assume  that  the  entire  weight  of  the  gate,  100  pounds,  is 
acting  at  its  center  C,  and  let  us  compute  the  moments  about  the  lower 
hinge  B.     The  moment  of  this  weight  about  B  is  100  times  2.5  (the 
perpendicular  distance  from  B  to  the  line  of  action  CW  of  the  weight). 
The  moment  about  the  lower  hinge  B  of  the  horizontal  pull  X\  exerted 
by  the  upper  hinge  A  is  3  times  X\.     Making  these  two  moments  equal 
we  have 

3  X  Xi  =  2.5  X  100 
and  Xi  =  83.3  pounds. 

(c)  In  a  similar  way  we  may  assume  the  upper  hinge  A  to  be  a 
fulcrum,  and  may  compute  the  push  X2  exerted  by  the  lower  hinge. 
Thus  we  have 

3  X  X2  =  2.5  X  100 
v  and  Xz  =  83.3  pounds. 

Notice  that  in  paragraphs  (b)  and  (c)  we  have  not  considered  the 
vertical  forces  YI  and  F2.    Why  is  it  not  necessary  to  do  so? 


BENT  LEVER 


29 


Fig.  30.  Automobile 
foot  brake  is  a  bent 
lever. 


QUESTIONS  AND  PROBLEMS 

1.  A  trade  catalogue  advertises  a  certain  "hammer  with  a  mighty 
pull."     It  claims  that  a  force  of  50  pounds  on  the  handle  exerts  a  pull 
of  1100  pounds  on  a  nail.     If  the  handle  is  12  inches  long,  what  is  the 
distance  between  the  nail  and  the  fulcrum?     How  does  this  distance 
change  as  the  nail  is  pulled  out  ?     What  effect  does  this  change  have  on 
the  pull  exerted  on  the  nail?      Illustrate  your 

answer  by  sketches. 

2.  A  rectangular  door  7  feet  high  and  4  feet 
wide  has  its  center  of  gravity  at  its  geometrical 
center.    It  is  hung  on  hinges  placed  1  foot  from 
the  top   and  bottom.      The  door  weighs  60 
pounds,     (a)  What  is  the  vertical  force  exerted 
by  each  hinge?     (6)     What  is  the  horizontal 
pull  exerted  by  the  upper  hinge?     (c)    What 
is  the   horizontal  push  exerted  by  the  lower 
hinge  ? 

3.  Suppose  the  door   in    problem  2    were 
turned  around  so  as  to  be  4  feet  high  and  7  feet 

wide,  the  hinges  being  placed  3  inches  from  the  top  and  bottom  respect- 
ively. (a)  Will  this  change  the  vertical  forces  exerted  by  each  hinge  ? 
(6)  Will  this  change  the  horizontal  forces?  (c)  In  which  case  are  the 
stronger  hinges  required? 

4.  The  foot  brake  on  a  certain  automobile  has  the  shape  shown  in 

figure  30.  It  turns  about  a  fixed  point  F,  and  when 
the  foot  presses  on  the  pedal  F,  there  is  a  much 
greater  force  exerted  on  the  rod  R.  Indicate  on  a 
sketch  just  how  you  would  compute  the  moment 
of  the  effort  and  the  moment  of  the  resistance. 
What  is  the  mechanical  advantage  of  the  lever  shown 
in  figure  30?  (Measure  dimensions.) 

6.  On  the  same  automobile  the  brake  rod  is 
attached  to  another  bent  lever  (AF  in  figure  31) 
so  that  a  push  P  exerted  at  A  tends  to  contract 
fae  brake  band  BE'  around  the  outside  of  a  drum 

on  the  rear  wheeh       Show  by  a   sketch   how  you 
bile  brake  band,    would  compute  the  contracting  force  (that  is,  the 
force  which  brings  B  and  B'  nearer  together)  if  you 
knew   the  push  at  A   and  the  dimensions   of  the  lever. 


bent 


30  SIMPLE  MACHINES 


PRACTICAL  EXERCISE 

Automobile  brake  levers.  Investigate  how  the  emergency  or  hand 
brake  on  some  automobile  works.  Make  a  sketch  showing  the  dimen- 
sions. Compute  the  mechanical  advantage  of  each  lever  involved. 

27.  Wheel  and  axle.    A  special  form  of  lever  consists  of  a 

wheel  or  crank  which  is  fastened  rigidly  to  an 
axle  or  drum.  The  weight  to  be  lifted,  or  the 
resisting  force  of  whatever  kind,  is  generally 
applied  to  the  axle  by  means  of  a  rope  or  chain, 
and  the  effort,  or  pull,  is  exerted  on  the  rim 
of  the  wheel,  as  shown  in  figure  32.  In  calcu- 
lating the  effort  E  needed  to  balance  a  given 
resistance  W,  we  have  merely  to  take  moments 
about  the  center  F  of  the  wheel  and  axle.  If  we 
Fig.  32.  Wheel  call  the  radius  of  the  wheel  R  and  that  of  the 
axle  r,  then, 

Weight  X  axle-radius  =  effort  X  wheel-radius 
or  W  Xr  =E  X  R 

W    R 
-  =  -. 

In  words  this  may  be  stated  thus :  the  weight  lifted  on  the 
axle  is  as  many  times  the  force  applied  to  the  wheel  as  the  radius 
6f  the  wheel  is  times  the  radius  of  the  axle.  Therefore  the  me- 
chanical advantage  of  the  wheel  and  axle  is  equal  to  the  radius 
of  the  wheel  divided  by  the  radius  of  the  axle. 

It  will  be  useful  to  remember  that  the  diameters  or  circumferences 
of  the  wheel  and  axle  bear  the  same  ratio  as  their  respective  radii. 

28.  Uses  of  the  wheel  and  axle.     A  windlass  used  in  drawing 
water  from  a  well  by  means  of  a  rope  and  bucket  is  an  appli- 
cation of  the  principle  of  the  wheel  and  axle.     In  the  windlass 
a  crank  takes  the  place  of  a  wheel,  and  the  length  of  the 
crank  corresponds  to  the  radius  of  the  wheel. 


THE   PULLEY 


31 


FOR  EXAMPLE,  suppose  we  wish  to  lift  a  load  of  75  pounds  with 
a   windlass    (Fig.    33)    whose    drum   is   6   inches  in   diameter  and 
whose  crank  handle  is  15  inches  from 
the    center    of   the  drum.       Since  the 
radius  of  the  axle  is  3  inches,  we  have 


and 


15  X  E  =  3  X  75 

E  =  15  pounds. 


Another  application  of  the  wheel 
and  axle  is  the  capstan.  In  this 
case,  the  axle  or  drum  is  vertical  and 
the  effort  is  sometimes  applied  by 
means  of  handspikes.  On  modern 


Fig.  33.    Diagram  of  a  windlass. 


ships,  steam  or  electric  power  is  used 
to  rotate  the  drum.  The  steering  wheel  on  a  boat,  the  hand 
wheel  used  on  the  brake  of  a  freight  or  street  car,  and  numerous 
devices  about  the  house,  such  as  the  ice-cream  freezer,  bread 

mixer,  wringer,  and  door  knob, 
are  also  examples  of  the  wheel 
and  axle. 

29.  The  pulley.  The  fixed 
pulley,  shown  in  figure  34,  con- 
sists of  a  wheel  with  a  grooved 
rim,  called  a  sheave,  free  to 
rotate  on  an  axle  which  is  suj>- 
ported  in  a  fixed  block.  A 
flexible  rope  or  cable  passes  over 
the  wheel.  It  is  evident  that  if 
equal  weights  or  equal  forces  are 
applied  to  the  ends  of  the  rope, 
they  just  balance  each  other. 
That  is,  the  effort  E  is  equal  to  the  load  or  resistance  W,  and 
therefore  the  mechanical  advantage  in  the  fixed  pulley  is  1. 
However,  it  is  sometimes  more  convenient  to  exert  a  certain 
pull  downwards  rather  than  upwards. 

Oftentimes  the  block  is  attached  to  the  weight  to  be  lifted, 


Fig.  34.     Fixed  pulley. 


32 


SIMPLE  MACHINES 


as  shown  in  figure  35,  and  then  it  is  called  a  movable  pulley. 

Here  the  effort  E  is  not  equal  to  the  weight  W,  for  it  will  be 

seen  that  the  load  W  is  supported 
by  two  ropes,  and  therefore  each 
exerts  an  upward  pull  equal  to  one 
half  the  weight.  That  is, 


W 
- 


W 
- 


Fig.  35.     Movable  pulley. 


Therefore,  the  mechanical  ad- 
vantage of  a  single  movable  pul- 
ley is  2. 

30.  Combinations  of  pulleys.  In 
practical  work  it  is  common  to  use 
both  fixed  and  movable  pulleys, 
such  as  a  fixed  block  with  two 
sheaves  and  a  movable  block  with 

two  sheaves,  as  shown  in  figure  36.     One  end  of  the  rope  is 

attached  to  the  fixed  block,  and  the  effort  is  applied  to  the 

other  end  of  the  rope.    Let  us  compute  the  relation  between  the 

weight  to  be  lifted  and  the  effort  applied. 

From  figure  36  it  will  be  seen  that  the 

weight  and  the  movable  block  are  sup- 

ported by  four  ropes,  and  so  the  pull 

on  each  rope,  neglecting   the  weight 

of  the  block,  is  one  fourth  the  weight  W. 

It  will  also  be  seen  that  the  pull  E  is 

equal  to  that  in  each  of  the  rcpes, 

since  a  fixed  pulley  changes  only  the 

direction  of  the  pull.     Therefore 


E  = 


W 


Fig.  36.     Two  double  blocks, 

and  the  mechanical  advantage  W/E  is  4. 

This  means  that,  if  friction  and  the  weight  of  the  movable 


PARALLEL  FORCES  IN  GENERAL  83 

block  are  disregarded,  a  pull  of  100  pounds  applied  at  E  would 
just  balance  a  weight  of  400  pounds  at  W. 

In  general,  we  can  find  the  mechanical  advantage  of  any  pair 
of  pulleys  by  counting  the  number  of  ropes  acting  on  the  movable 
block. 

31.  Parallel  forces  in  general.  In  many  of  the  machines  so 
far  studied,  for  example  the  wheelbarrow  with  one  or  two 
loads,  the  coal  shovel,  and  sometimes  the  wheel  and  axle,  all 
the  forces  acting  are  parallel  to  each  other.  In  all  these  cases 
two  general  principles  are  in- 
volved, which  sum  up  all  that 
we  have  learned.  A  simple  ex- 
periment will  make  these  prin- 
ciples clear. 

Hang  a  light  stick  (Fig.  37)  by 
two  or  more  stirrups  attached  to 
spring  balances  A,  B,  C,  and  let 
several  weights  D,  E  be  hung  from 
it  at  various  points.  By  reading  Fig'  37'  P*™llelforces. 

the  balances  it  will  be  easy  to  check  up  the  fact  that  the  sum  of  the 
forces  pulling  up  is  equal  to  the  sum  of  the  forces  pulling  down.  Even 
without  doing  the  experiment  we  could  have  foreseen  that  this  must 
be  true,  because  if  either  set  of  forces  overbalanced  the  other,  the  stick 
would  move. 

Now  suppose  that  there  happen  to  be  several  holes  through  the  stick 
and  that  a  nail  is  carefully  driven  through  one  of  them  into  the  wall 
behind.  Then  think  of  the  nail  as  the  fulcrum  of  a  lever,  and  compute 
the  moments  of  all  the  forces  tending  to  turn  the  stick  clockwise  about 
the  nail  and  the  moments  of  those  tending  to  turn  it  counterclockwise. 
It  will  be  found  that  these  two  sets  of  moments  just  equal  each  other. 
Here  also  we  could  have  foreseen  that  this  must  be  true,  because  if 
either  set  of  moments  overbalanced  the  other,  the  stick  would  begin  to 
turn  around  the  nail. 

Evidently  the  nail  could  have  been  put  through  a  hole  at  any  point 
along  the  stick.  So  the  moments  calculated  around  any  point  must 
balance. 

This  experiment  shows  that  when  several  parallel  forces 
are  in  equilibrium,  two  conditions  must  be  fulfilled : 


A  3000  Ibs. 


34  SIMPLE  MACHINES 

t 

(1)  The  sum  of  the  forces  pulling  in  one  direction  must  equal 
the  sum  of  the  forces  pulling  in  the  opposite  direction. 

(2)  The  sum  of  the  moments  tending  to  rotate  the  body  in  one 
direction  around  any  point  whatever  must  equal  the  sum  of  the 
moments  tending  to  rotate  the  body  in  the  opposite  direction  around 
the  same  point. 

These  two  statements  are  so  important  that  they  may  well 
be  memorized. 

FOE  EXAMPLE,  suppose  that  a  3000-pound  automobile  is  standing  on 
a  bridge  one  fourth  of  the  way  across  (Fig.  38)  and  that  we  wish  to  know 
,— ^  how  much  of  its  weight 

\c  ^jlj^&5jjj  \B       A  is  carried  by  each  of 

the  supports  at  the  ends 
of  the  bridge.  Let  B 
and  C  be  the  two  up- 
ward forces  the  magni- 
3x  •  *•//  tudes  of  which  are  to 

Fig.  38.    Bridge  with  automobile  on  it.  he  found.     Suppose  we 

use  principle  (2)  above, 

and  take  moments  around  the  left-hand  end  of  the  bridge,  where  C 
acts.     Then  C  has  no  moment  and  we  have 

B  X  4  x  =  3000  X  x 

B  =  750  pounds. 

Next,  using  principle  (2)  again,  take  moments  around  the  right-hand 
end,  where  B  acts.     We  have 

C  X  4x  =  3000  X  3x 
C  =  2250  pounds. 

Finally,  we  use  principle  (1)  above  as  a  check  on  the  correctness  of  our 
numerical  work.     We  should  have 

B  +  C  (upward)  =  A  (downward), 
which  checks  because  750  +  2250  =  3000. 

PROBLEMS 

(It  will  greatly  assist  in  the  solution  of  these  problems  to  draw  a  careful  diagram 

in  each  case.) 

1.  The  diameter  of  an  axle  is  1  foot,  and  the  diameter  of  the  circle 
in  which  a  crank  on  the  axle  moves  is  3  feet.  If  150  pounds  is  the 
weight  to  be  raised,  how  much  force  must  be  applied  to  the  crank  ? 


PARALLEL  FORCES  IN  GENERAL 


35 


2.  The  crank  on  a  grindstone  is  9  inches  long,  and  the  diameter  of 
the  stone  is  30  inches.     If  50  pounds  is  the  force  applied  on  the  crank, 
what  force  can  be  exerted  on  the  rim  of  the  stone  ? 

3.  What  must  be  the  ratio  of  the  diameters  of  a  wheel  and  axle  in 
order  that  an  effort  of  150  pounds  may  support  a  load  of  1  ton  ?     What 
is  the  mechanical  advantage  ? 

4.  Two  single  fixed  pulleys  are  used  to  raise  a  barrel  of  flour,  as 
shown  in  figure  39.     If  the  barrel  of  flour  weighs  200 

pounds,  how  much  does  the  horse  have  to  pull? 

6.  The  sail  of  a  boat  is  to  be  raised  by  means  of  a 
movable  single  block  attached  to  the  gaff  and  a  fixed 
double  block  attached  to  the  top  of  the  mast,  one  end 
of  the  rope  being  tied  to  the  movable  block.  How  much 
resistance  can  be  overcome  by  100  pounds  exerted  on 
the  rope  ? 

6.  A  pair  of  triple  blocks  (three  sheaves  in  each 
block)  is  used  to  raise  a  1-ton  weight. 

The  rope  is  attached  to  the  upper 
fixed  block.  What  effort  must  be 
applied?  Disregard  friction. 

7.  An  automobile  gets  stuck  in 


SimPle  Pulley  system- 


the  sand.  In  order  to  pull  it  out,  a  horse,  a  rope,  and  a  pair  of  triple 
blocks  are  used.  If  the  horse  exerts  a  steady  pull  of  200  pounds  on 
the  rope,  and  one  block  is  fastened  to  a  tree  and  the  other  to  the 
machine,  how  much  resistance  can  be  overcome?  Find  two  solutions 
for  this  problem,  the  rope  being  fastened  in  one  case  to  the  fixed 
block,  and  in  the  other  to  the  movable  block. 

8.  Two  boys,  A  and  B,  are  carrying  a  100-pound  load  slung  on  a 
pole  between  them.     Their  hands  are  10  feet  apart,  and  the  load  is  3  feet 
from  A.     How  much  does  each  carry?     Neglect  the  weight  of  the 
pole. 

9.  A  man  holds  a  shovelful  of  coal  with  his  left  hand  at  the  end  of 
the  shovel  and  his  right  hand  22  inches  away.     Suppose  the  center  of 
gravity  of  the  shovel  and  coal  to  be  40  inches  from  his  left  hand,  and 
the  weight  of  the  shovel  and  coal  to  be  50  pounds.     How  much  does  he 
push  down  with  his  left  hand,  and  how  much  does  he  pull  up  with  his 
right  hand  ? 

10.  A  man  and  a  boy  carry  a  load  of  200  pounds  on  a  pole  8  feet 
long.  Where  must  the  load  be  placed  if  the  boy  is  to  bear  only  45 
pounds  of  it  ? 


36 


SIMPLE   MACHINES 


11.  How  much  must  a  boy  lift  on  each  handle  of  a  wheelbarrow  if 
the  center  of  gravity  of  the  120-pound  load  is  15  inches  from  the  axle 
and  his  hands  are  25  inches  farther  away?     Assume  that  the  wheel- 
barrow weighs  50  pounds  and  has  its  center  of  gravity  12  inches  from 
the  axle.     Compute  also  the  force  exerted  by  the  axle. 

12.  What  is  the  smallest  number  of  pulleys  required  to  lift  a  weight 

of  500  pounds  with  an  effort  of  100  pounds  ? 
How  should  they  be  arranged  ? 

13.  The  hoisting  derrick  shown  in  figure 
40  consists  of  a  windlass  with  gears.    The 
drum  has  a  diameter  of  8  inches  and  a  large 
cogwheel  with  60  cogs  ;  the  pinion,  or  small 
cogwheel,  has  10  cogs,  and  the  crank  radius 
is  18  inches.      What  is  the  mechanical  ad- 
vantage of  this  double  wheel  and  axle  ? 

14.  A  bridge   100  feet  long  weighs  200 
tons  and  has  its  center  of   gravity  in  the 
middle.      A  locomotive  weighing  100  tons 
stands  on  the  bridge  with  its  center  of  grav- 
ity 40  feet  from  the  north  end.     What  is 
the  stone  abutment   at   each  end   has   to 

PRACTICAL  EXERCISE 


Fig.  40.  Hoisting  derrick  is 
a  double  wheel  and  axle. 

the  total  weight  which 
support  ? 


Center  of  gravity  of  an  automobile.  Weigh  an  automobile.  Find 
out  how  much  of  this  weight  is  carried  on  the  rear  wheels.  Compute 
how  far  back  of  the  front  axle  the  center  of  gravity  is  located.  Can  you 
think  of  any  method  of  determining  how  high  the  center  of  gravity  is 
above  the  ground  ? 

32.  Work.  The  function  of  every  machine  is  to  do  a  certain 
amount  of  work.  Now  in  the  technical  language  of  science, 
work  means  the  overcoming  of  resistance.  For  example 
(Fig.  41),  a  man  does  work  when  he  lifts  a  trunk  from  the 
platform  into  a  truck,  or  when  he  drags  the  trunk  along  the 
platform.  But  the  man  does  not  do  work  in  the  scientific 
sense  of  the  word,  no  matter  how  hard  he  pushes  or  pulls,  if 
he  does  not  lift  or  move  the  trunk.  In  other  words,  work  is 
measured  by  accomplishment,  not  by  effort  or  by  fatigue. 


PRINCIPLE  OF   WORK  37 

If  we  lift  one  pound  a  vertical  distance  of  one  foot,  we  are 
said  to  do  one  foot  pound  of  work;  if  we  lift  100  pounds 
3  feet,  we  do  300  foot  pounds  of  work ;  or  if  we  exert  a  force 


EXPRESS  Co. 

-10  ft: 


so  Ibs. 


Work  done  in  lifting  box  Work  done  in  dragging  box 

'  '   3X100=800  ft.  Ibs.  10x30  =  300  ft.  Ibs. 

Fig.  41.     Examples  of  doing  work. 

of  30  pounds  on  a  100-pound  box  and  thus  drag  it  10  feet, 
we  still  do  300  foot  pounds  of  work.     In  other  words, 

Work  (foot  pounds)  =  force  (pounds)  X  distance  (feet). 

It  should  be  remembered  that  the  distance  must  be  meas- 
ured in  the  same  direction  as  that  in  which  the  force  is  exerted. 

FOR  EXAMPLE,  if  a  machinist  exerts  upon  a  file  a  force  of  10  pounds 
downward  and  15  pounds  forward,  how  much  work  will  he  do  in  40 
horizontal  strokes,  each  6  inches  long?  Evidently  the  total  distance 
is  20  feet  and  the  horizontal  force  is  15  pounds  ;  therefore  the  work  done 
is  300  foot  pounds.  Since  the  downward  push  produces  no  motion 
but  merely  serves  to  produce  friction  between  the  file  and  the  surface 
being  filed,  no  work  in  the  scientific  sense  is  done  by  maintaining  the 
downward  push  of  10  pounds. 

33.  Principle  of  work.  In  every  machine  a  certain  resistance 
is  overcome  by  a  certain  effort  exerted  on  another  part  of 
the  machine.  The  principle  of  work,  which  applies  to  all 
machines  where  the  losses  due  to  friction  may  be  neglected, 
may  be  stated  as  follows :  The  work  put  into  a  machine  is  equal 
to  the  work  got  out.  In  short, 

Input  =  output. 

FOR  EXAMPLE,  in  the  wheel  and  axle  (Fig.  32)  the  output  is  equal  to 
the  weight  times  the  distance  it  is  lifted,  and  the  input  is  equal  to  the 
effort  times  the  distance  through  which  it  is  exerted.  For  convenience, 
suppose  the  wheel  makes  just  one  turn.  Then  the  distance  the  weight 


38  SIMPLE  MACHINES 

is  lifted  is  equal  to  the  circumference  of  the  axle,  2irr,  and  the  distance 
through  which  the  effort  is  exerted  is  the  circumference  of  the  wheel, 
2irR.  The  input  is  E  X  2*R,  and  the  output  is  W  X  2irr.  There- 
fore, by  the  principle  of  work, 

E  X  2irR  =  W  X  2irr 
or  E  X  R  =  W  X  r, 

which  is  exactly  the  equation  got  by  considering  the  wheel  and  axle  as 
a  modified  lever. 

Another  example  is  the  system  of  pulleys  shown  in  figure  36.  The 
output  is  equal  to  the  weight  W  times  the  distance  it  is  lifted,  and  the 
input  is  equal  to  the  effort  E  times  the  distance  through  which  it  is 
exerted.  Suppose  the  distance  the  weight  W  is  lifted  is  D,  and  the 
distance  through  which  the  effort  E  is  exerted  is  d.  The  output  is 
W X  D  and  the  input  is  EXd.  Then,  by  the  principle  of  work, 

W  X  D  =  E  X  d 
W        d 
-E   =  IT 

But  when  the  weight  is  lifted  1  foot,  it  is  evident  that  each  of  the  sup- 
porting ropes  must  be  shortened  by  1  foot,  and  therefore  E  must  move 
4  feet ;  in  other  words, 

d  =  4Z>. 

Substituting  this  value  of  d  in  the  preceding  equation,  we  have 

W 

¥  =  4' 

which  is  the  same  as  the  result  which  we  got  in  section  30. 

PROBLEMS 

1.  How  much  work  does  a  man  do  in  lifting  a  150-pound  trunk  into 
a  truck  which  is  3.5  feet  above  the  ground  ? 

2.  A  man  carries  in  baskets  a  ton  of  coal  up  20  steps,  each  7  inches 
high.     How  much  work  does  he  do  on  the  coal  ? 

3.  In  the  metric  system  work  is  measured  in  kilogram  meters.     How 
much  work  is  done  in  pumping  50  liters  of  water  40  meters  high  ? 

4.  A  horse  weighing  1200  pounds  draws  a  loaded  wagon  weighing 
one  ton  10  miles  in  4  hours.     If  the  average  pull  exerted  by  the  horse 
is  130  pounds,  how  much  work  does  the  horse  do  ? 

5.  A  girl  weighing  125  pounds  climbs  to  the  top  of  Bunker  Hill  mon- 
ument, which  is  220  feet  high.     How  much  work  does  she  do  ? 


THE   DIFFERENTIAL   PULLEY 


39 


6.  How  much  work  does  a  man  do  in  filling  a  100-gallon  water  tank 
the  average  height  of  which  is  30  feet  above  the  well  ? 

7.  Experiment  shows  that  it  requires  50  pounds  to  push  a  150-pound 
packing  case  along  the  floor.     How  much  work  is  done  in  pushing  this 
case  3  yards  ?  in  lifting  it  vertically  3  yards  ? 

8.  A  man  weighing  150  pounds  pulls  himself  up  a  mast  in  a  sling  by 
means  of  a  rope  passing  over  a  fixed  pulley  at  the  top  of  the  mast.    How 
much  work  does  he  do  while  rising  100  feet?     How  hard  must  he  pull  ? 

34.  The  differential  pulley.  In  shops  where  heavy  machin- 
ery is  to  be  lifted,  use  is  often  made  of  the  differential  pulley, 
shown  in  figure  42.  This  con- 
sists of  two  sheaves  of  different 
diameters  in  the  upper  block 
rigidly  fastened  together,  and 
one  sheave  in  the  lower  block. 
An  endless  chain  runs  over  these 
blocks.  The  rims  of  the  sheaves 
of  the  upper  block  have  projec- 
tions which  fit  between  the  links 
and  so  keep  the  chain  from  slip- 
ping. Such  a  differential  pulley 
has  a  very  large  mechanical 

advantage.  Fig.  42.     Differential  pulley. 

To  see  just  how  it  comes  to  have  a  large  mechanical  advantage,  let 
us  set  up  such  a  pulley  and  study  it  carefully.  When  the  chain  is  pulled 
down  as  shown  in  the  diagram,  it  is  wound  up  faster  on  the  large  fixed 
pulley  than  it  is  unwound  on  the  smaller  pulley.  In  order  to  compute 
the  mechanical  advantage  of  the  contrivance,  let  us  suppose  that  E 
moves  down  far  enough  to  turn  the  fixed  pulley  around  once.  If  R  is 
the  radius  of  the  large  fixed  pulley,  then  the  work  done  by  E  will  be 
E  X  2irR.  If  r  is  the  radius  of  the  small  fixed  pulley,  then  the  length 
of  chain  unwound  in  one  revolution  will  be  2-rr.  The  weight  W  will 
therefore  be  raised  ^(2-n-R  —  2-n-r),  or  ir(R  —  r),  and  the  work  done 
will  be  W  X  ir(R  —  r}.  Therefore,  if  we  neglect  losses  due  to  friction, 


whence 


W  X  -K(R-r)  =  E  X  2wR 
W      2  R 
E  ~ R-r 


40 


SIMPLE  MACHINES 


Since  the  difference  between  the  radii  of  the  two  fixed  pul- 
leys (R—r)  is  small,  it  is  evident  that  the  mechanical  advan- 
tage is  large. 

The  differential  pulley  has  a  second  practical  advantage  in 
that  there  is  always  enough  friction  to  keep  the  weight  from 
dropping  when  the  force  E  is  released. 

35.  Inclined  plane.  Barrels  and  casks  which  are  too  heavy 
to  lift  from  the  ground  into  a  wagon  are  often  rolled  up  a  plank 
or  skid.  This  is  an  example  of  what  is  called  an  inclined  plane. 
Every  street  or  road  which  is  not  level  is  an  example  of  an 
inclined  plane.  Experience  teaches  us  that  the  steeper  the 
incline,  the  greater  the  pull  required  to  haul  the  load  up  the 

grade.  In  order  to 
find  out  just  how  the 
effort  and  the  weight 
or  load  are  related  to 
the  grade,  let  us  try 
a  simple  experiment 
where  friction  can  be 
\E  neglected. 


w 


Fig.  43.     Inclined  plane. 


Suppose  we  arrange 
a  very  smooth  plane  at 
an  angle,  as  shown  in 
figure  43.  Let  the  weight  or  load  W  be  a  heavy  metal  cylinder  which 
rolls  with  very  little  friction.  Attach  to  the  cylinder  a  cord  and  pass 
it  over  a  pulley  fastened  to  the  top  of  the  plane,  and  then  hang  on  the 
other  end  enough  weights  to  pull  the  load  slowly  up  the  inclined  plane. 
You  will  find  that  the  ratio  W/E  is  approximately  the  same  as  the 
ratio  LI  H,  where  L  is  the  length  of  the  incline  and  H  is  its  height. 

From  the  general  principle  of  work  we  can  also  arrive  at 
this  relation  of  resistance  and  effort  to  the  length  and  height 
of  the  incline.  Suppose  the  weight  W  is  rolled  from  the  bottom 
to  the  top  of  the  incline.  Then  it  has  been  lifted  H  feet,  and 
the  work  done  is  W  (pounds)  times  H  (feet),  or  WH  foot 
pounds.  But  while  the  weight  W  has  been  traveling  up  the 


WEDGE  41 

incline  whose  length  is  L,  the  effort  E  has  moved  L  feet,  and 
the  work  put  in  is  equal  to  E  (pounds)  times  L  (feet),  or  EL 
foot  pounds.  Therefore,  if  we  neglect  friction,  we  have 


WX  H=  E  X  L 
W      L 


36.  The  grade  of  an  incline.     A  civil  engineer  measures  his  dis- 
tances horizontally  and  vertically,  and  when  he  speaks  of  a  1  per  cent 
grade,  he  means  an  incline  which  rises  1  foot  per  hundred  feet  measured 
horizontally.     In  other  words,  the  grade  of  an  incline  is  the  ratio  of  the 
height  to  the  base  expressed  as  per  cent.     For  example,  suppose  a  road 
rises  5  feet  for  every  100  feet  measured  horizontally,  then  this  road  is 
said  to  have  a  5%  grade.     Since  a  3%  grade  is  the  steepest  allowable 
on  a  really  good  road,  it  is  readily  seen  that  a  small  force,  such  as  can 
be  exerted  by  a  horse,  can  move  a  much  heavier  load  up  a  gradual  in- 
cline than  could  be  lifted  directly.     For  this  reason  the  highways  in 
mountain  regions  are  laid  out  as  zigzags  and  switchbacks.     If  we  want 
a  flight  of  steps  easy  to  climb,  we  make  the  slope  gentle. 

Nevertheless  it  should  be  remembered  that  while  the  pull  is  less  than 
the  weight  of  the  load,  yet  the  distance  the  load  travels  is  greater  than 
when  it  is  lifted  straight  up.  In  other  words,  what  we  gain  in  the 
amount  of  effort  required  we  lose  in  the  distance  over  which  it  must  be 
exerted.  The  total  work  to  be  done  is  independent  of  the  grade,  except 
for  the  indirect  effect  of  friction. 

37.  Wedge.     If  instead  of  pulling  the  load  up  the  incline,  we 
push  the  incline  under  the  load,  the  inclined  plane  is  called 
a  wedge.     Of  course  the  smaller  the  angle  of  the  wedge,  the 
easier  it  is  to  push  it  in  under  the  resistance.     The  fact  that 
friction  plays  a  very  important  part   makes   it  impossible  to 
state  simply  the  relation  between  the  effort  required  to  force 
in  a  wedge  and  the  resistance  to  be  overcome. 

All  cutting  and  piercing  instruments,  such  as  the  ax,  the 
chisel,  and  the  carpenter's  plane,  as  well  as  nails,  pins,  and 
needles,  act  like  wedges.  The  carpenter  uses  wedges  to  fasten 
the  heads  of  hammers  and  axes  on  their  handles.  The  woods- 
man uses  wedges  to  split  logs  of  wood. 


42 


SIMPLE  MACHINES 


Piston 


In  many  machines  rotating  wedges,  or  cams,  are  used  to  exert 
pushes  on  rods.  For  example,  a  very  common  way  of  opening  the  in- 
take and  exhaust  valves  of  an  auto- 
mobile engine  is  to  arrange  the  valve 
stems,  or  rods,  so  that  they  are  pushed 
up  at  the  proper  instant  by  a  rotating 
cam,  as  shown  in  figure  44. 

38.  Screw.  When  an  enormous 
force  must  be  exerted,  as  in  lift- 
ing a  building,  such  machines  as 
the  lever  and  pulley  will  not  do, 
because  we  cannot  get  enough 
mechanical  advantage.  A  screw, 
such  as  the  jackscrew,  is  used  for 
this  purpose. 

One  form  of  jackscrew,  used  to  lift 
the  axle  of  an  automobile,  is  shown 
in  figure  45.  The  screw  itself  does 
not  rotate,  but  the  nut  is  slowly  turned  so  as  to  raise  the  load.  In 
one  complete  turn  of  this  nut  the  screw  is  lifted  the  distance  between 
two  successive  threads.  The  effort  is  applied 
at  the  end  of  the  handle.  The  two  equal 
bevel  gears  between  the  handle  and  the  nut 
enable  one  to  push  downward  instead  of  side- 
wise.  They  may  be  ignored  and  the  handle 
thought  of  as  attached  directly  to  the  nut. 


Fig.  44.    Cams  used  to  open  valves 
on  automobile  engine. 


The  pitch  of  a  screw  is  the  distance 
between  two  successive  threads.  In  each 
complete  turn  of  a  screw  the  output  is 
equal  to  the  weight  times  the  pitch,  and 
the  input  is  equal  to  the  effort  times 
the  distance  through  which  it  acts; 
namely,  the  circumference  of  a  circle  Fi«-  45-  Automobile  jack- 
made  by  the  end  of  the  handle. 

If  W  equals  the  weight  to  be  lifted  and  p  (pitch)  equals 
the  distance  between  threads,  the  output  for  one  turn  is  W 


APPLICATIONS  OF   THE  SCREW 


43 


times  p.  Let  E  equal  the  effort  or  force  applied  on  the  handle, 
and  2  irr  equal  the  circumference  of  the  circle  in  which  it  acts. 
Then  E  times  2  trr  is  the  input.  Therefore,  applying  the  prin- 
ciple of  work  to  the  machine,  we  have,  if  friction  could  be 
neglected, 

WXp=EX2irr 
W        2  Trr 


Fig.  46.  Machin- 
ist's vise.  The 
screw  is  turned 
by  a  lever. 


In  other  words,  the  mechanical  advantage  of  the  screw  is  equal 

to  the  ratio  of  the  circumference  of  the  circle  moved  over  by  the 

end   of  the   lever,   to   the   distance  between  the 

threads  of  the  screw. 
As  a  matter  of  fact,  friction   consumes  a 

large  part  of  the  work  put  in,  and  therefore 

the  input  is  greater  than  the  output.     But  this 

loss  is  not  wholly  a  disadvantage,  for  friction 

keeps    a    screw   from   turning   backward    of 

itself. 

39.  Applications  of  the  screw.    We  are  all 

familiar    with    carpenters'    wood    screws   and 

machinists'  bolts.      Most  of  us  have  seen  a  machinist's  vise 

(Fig.  46),  which  uses  a  screw  operated  by  a  lever.     Ordinarily, 

however,  we  do  not  think  of  the  propeller  of  a  boat  or  air- 
plane as  a  screw,  but  it  is. 
The  propeller  of  a  boat 
(Fig.  47),  with  its  two, 
three,  or  four  blades  fastened 
to  one  end  of  the  shaft,  is 
driven  by  an  engine  at  the 
other  end.  Its  rotation  is 
so  rapid  that  the  water  has 
no  time  to  get  out  of  the 


o 


T 

Fig.  47.     Screw  propeller  on  a  boat. 


way,  and  the  propeller  screws  itself  through  the  water  like  a 
wood  screw  through  wood.      Another  example  of  the  screw  is 


44 


SIMPLE  MACHINES 


Fig.  48.  A  micrometer  screw  meas- 
ures to  o.ooi  of  a  millimeter. 


the  micrometer  screw  (Fig.  48),  which  is  used  to  make  very 
precise  measurements.     It  contains  an  accurately  turned  thread 

of  very  small  pitch,  perhaps  1 
millimeter.  It  is  evident  that 
if  such  a  screw  is  turned  1Q0 
of  a  complete  turn,  the  spindle 
moves  along  its  axis  just  0.01 
millimeters.  This  is  the  easiest 
way  to  measure  so  small  a  dis- 
tance. The  head  is  divided  into  100  divisions,  so  as  to  indi- 
cate quickly  and  accurately  the  fraction  of  a  revolution 
through  which  the  screw  has  been 
turned. 

40.  The  worm  gear.     A  worm  gear  is  another 
device  for  getting  a  large  mechanical  advan- 
tage.    It  consivSts  of  a  screw  thread  on  a  shaft 
which  is  tangent  to  a  cogwheel,  as  shown  in 
figure  49.     One  revolution  of  the  shaft  rotates 
the  cogwheel  the  distance  between  two  cogs. 
Therefore,  if  the  cogwheel  has  n  teeth,  the  shaft 
turns  n  times  as  fast  as  the  wheel.     Thus  the 
mechanical  advantage  of  such  a  worm  gear  is 
equal  to  the  number  of  teeth  on  the  wheel. 

This  device  is  commonly  used  to  drive  the  rear  axles  of  automobile 
trucks  (Fig.  50),  and  also  to  reduce  the  speed  in  speed  counters. 

41.  Combinations  of  simple  machines.    What  is  called  a 

single  machine  in  factories  and 
shops  is  usually  a  combination 
of  the  simple  machine  elements 
described  above.  That  is,  it  is 
a  more  or  less  complicated  col- 
lection of  levers,  pulleys,  wheels, 
axles,  screws,  and  gears. 

To  show  how  such  a  machine  may 
Fig.  50.     Worm  gear  as  used  on  the  be  analyzed  into  its  elements,  let  us, 
rear  axle  of  a  truck.  as  it  were,  dissect  a  crane,  or  derrick, 


49.     Model   of 
worm  gear. 


COMBINATIONS  OF  SIMPLE  MACHINES 


45 


(Fig.  51)  such  as  is  used  in  unloading  freight  cars,  or  in   hoisting 
building  material  into  place. 

The  movable  pulley  to  which  W  is  attached  gives  a  mechanical  ad- 
vantage of  2 ;  the  fixed  pulley  at  the  end  of  the  boom  merely  changes 
the  direction  of  the 
pull ;  the  wheel  F  and 
its  axle  G  give  a 
mechanical  advantage 
equal  to  the  ratio  of 
the  size  of  the  wheel 
to  the  size  of  the  axle. 
A  third  mechanical  ad- 
vantage is  gained  in 
the  wheel  and  axle,  D 
and  E,  a  fourth  ad- 
vantage is  gained  in 
B  and  C,  and  finally 
there  is  the  mechanical 
advantage  of  the  erank 
P  and  the  axle  A, 
The  total  mechanical 


mm 

Fig.  51.     Crane  used  in  freight  yards. 

advantage  of  this  compound  machine  is  the  product  (not  the  sum)  of 
the  separate  advantages  gained  by  its  separate  elements. 


In  general,  then,  to  compute  the  mechanical  advantage  of  any 
compound  machine,  first  find  the  mechanical  advantage  of  each 
separate  element  and  then  find  the  product  of  the  separate  advan- 
tages. Sometimes  it  is  simpler  to  compute  the  mechanical 
advantage  as  the  ratio  of  the  distance  the  effort  moves  to  the 
distance  the  resistance  or  load  moves  in  the  same  time.  This 
ratio  is  known  as  the  velocity  ratio. 


PROBLEMS 

(Friction  is  to  be  neglected  in  all  these  problems.) 

1.  What  force  will  be  needed  to  pull  a  weight  of  200  pounds  slowly 
up  a  slope  which  rises  1  foot  in  25  feet  measured  along  the  slope? 

2.  If  the  approach  to  a  bridge  rises  1  foot  in  10  feet  of  length,  how 
heavy  a  load  can  be  drawn  up  by  a  horse  that  can  exert  a  pull  of  * 
pounds? 


46  SIMPLE  MACHINES 

3.  A  boy  wants  to  roll  a  200-pound  barrel  of  flour  into  a  cart  4  feet 
above  the  ground.     He  can  push  with  a  force  of  80  pounds,     (a)   How 
long  a  plank  will  he  need  ?     (6)  How  much  work  does  he  do  ? 

4.  An  effort  of  40  pounds  acting  parallel  to  an  inclined  plane  is 
required  to  keep  a  250-pound  cake  of  ice  from  sliding  down.     What  is 
the  ratio  of  the  length  to  the  height  of  the  plane  ? 

6.  A  test  shows  that  it  takes  500  pounds  more  force  to  haul  an  elec- 
tric car  weighing  4  tons  up  a  certain  grade  than  to  haul  it  along  a  level. 
What  is  the  grade? 

6.  What  weight  can  be  raised  by  a  builder's  jackscrew  (Fig.  52) 
when  a  force  of  40  pounds  is  applied  at  the  end  of 
a  lever  arm  2  feet  long,  the  pitch  of  the  screw 
being  0.3  inches  ? 

7.  The  lever  in  a  jackscrew  extends  2  feet  from 
the  center.     If  a  man  is  able  to  lift  25  tons  by 
exerting  a  pressure  of  100  pounds,  how  many 
threads  to  the  inch  must  there  be? 

8.  In   the   preceding    problem,    what    is    the 
mechanical  advantage? 

Fig.  52.    Builder's  9     The  pitch  of  the  sorew  of  ft  bench  ^  (Fig> 

46)  is  0.2  inches  and  the  handle  of  the  screw  is 
7  inches  long.  What  force  could  be  exerted  by  the  jaws  of  the  vise  if 
a  force  of  25  pounds  were  applied  at  the  end  of  the  handle  ? 

10.  In  the  worm  gear  shown  in  figure  49,  the  wheel  G  has  98  teeth, 
and  its  drum  is  8  inches  in  diameter.     The  worm  is  turned  by  a  crank 
handle  E  which  is  15  inches  long,     (a)  What  is  the  velocity  ratio? 
(6)  How  great  a  weight  W  could  be  lifted  by  an  effort  of  20  pounds  ? 

11.  In  the  crane  shown  in  figure  51,  the  weight  W  is  5  tons,  and  the 
radii  of  the  four  small  cogwheels  are  assumed  to  be  equal  and  each 
1/5  the  radius  of  the  crank  P  and  of  the  wheels  B,  D,  and  F,  which  are 
also  assumed  to  be  equal,     (a)  What  is  the  mechanical  advantage  of 
the  whole  machine?     (6)  What  force  must  be  applied  at  P? 

12.  The  pedal  of  a  bicycle  is  halfway  down  and  is  pressed  down  with 
a  force  of  100  pounds.     The  crank  arm  is  6  inches  long,  and  the  sprocket 
wheel  is  8  inches  in  diameter.     Find  the  tension  or  pull  on  the  chain. 

13.  In  the  preceding  problem  the  sprocket  wheel  attached  to  the 
rear  wheel  is  2.5  inches  in  diameter,  and  the  wheel  is  28  inches  in  di- 
ameter,    (a)  How  far  does  the  bicycle  go  when  the  pedal  makes  one 
complete  revolution?     (&)  How  much  does  the  tire  of  the  rear  driving 


HORSE  POWER  47 

wheel  push  backward  on  the  roadbed  when  the  man  presses  100  pounds 
on  the  pedal  ? 

PRACTICAL  EXERCISE 

Automobile  jack.  Borrow  several  types  of  automobile  jacks  and 
measure  the  mechanical  advantage  of  each.  Is  a  large  mechanical 
advantage  a  real  advantage  ? 

42.  Work  and  power.     The  words  "  work  "  and  "  power  " 
are  often   confused   or  interchanged  in   colloquial  use.     The 
term  "work,"  in  physics,  means  the  overcoming  of  resistance. 
For  example,  if  a  boy  carries  a  pail  of  water  weighing  50  pounds 
up  a  flight  of  stairs  12  feet  high,  he  does  600  foot  pounds  of 
work.     The  amount  of  work  done  would  be  the  same  whether 
he  did  this  in  one  minute  or  one  hour,  but  the  amount  of  power 
required  to  do  this  job  in  one  minute  would  be  60  times  the 
power  required  to  do  it  in  one  hour.     The  term  "  power  " 
adds  the  idea  of  time.   Power  means  the  speed  or  rate  of  doing  work. 

43.  Horse  power.     The  earliest  use  of  steam  engines  was  to 
pump  water  from  mines.     This  work  had  previously  been  done 
by  horses  ;   so  the  power  of  the  various  engines  was  estimated 
as  equal  to  that  of  so  many  horses.    To  make  this  idea  definite, 
James  Watt  carried  out  some  experiments  to  determine  how 
many  foot  pounds  of  work  a  horse  could  do  in  one  minute. 
He  found  that  a  strong  dray  horse  working  for  a  short  time 
could  do  work  at  the  rate  of  33,000  foot  pounds  per  minute,  or 
550  foot  pounds  per  second.     This  rate  is  therefore  called  a 
horse  power.     To  get  the  horse  power  of  an  engine,  compute 
the  number  of  foot  pounds  of  work  done  per  minute  and  divide 
by  33,000,  or  per  second  and  divide  by  550. 

/TT  _  v       foot  pounds  per  minute 
Horse  power  (H.P.)  = 


foot  pounds  per  second 
550 


FOR  EXAMPLE,  an  engine  is  used  to  pump  10,000  gallons  of  water  per 
hour  into  a  reservoir  50  feet  above  the  supply.     How  much  horse  power 


is  required  ? 


48 


SIMPLE  MACHINES 


One  gallon  of  water  weighs  8.34  pounds ;  so  10,000  gallons  of  water 
weigh  83,400  pounds.  The  work  done  in  lifting  this  weight  50  feet  is 
83,400  X  50,  or  4,170,000  foot  pounds.  Since  this  is  done  in  one  hour, 
the  work  per  minute  is  4 1  Vo0  °  ° ,  or  69,500  foot  pounds.  The  horse 
power  required  would  be  tf|H$,  or  2.1  H.P. 

44.  Transmission  of  power.  In  any  shop  containing  several 
machines  one  easily  distinguishes  two  kinds  —  the  driving 
machines,  which  may  be  steam  or  oil  engines,  water  wheels,  or 
electric  motors,  and  the  driven  machines,  such  as  lathes,  drills, 
planers,  and  saws.  There  must  always  be  some  connecting 
link  between  a  driving  and  a  working  machine ;  that  is,  some 
means  of  transmission.  If  these  machines  are  not  far  apart, 

the  common  method  is  to 
use  shafting,  belts,  chains,  or 
cogwheels;  but  when  the 
1 1  prime  mover  and  the  driven 
machine  are  widely  separated, 
sometimes  even  miles  apart, 
some  form  of  electrical  trans- 
mission is  used.  Electrical 
transmission  will  be  explained 
in  Chapter  XVIII. 

When  a  belt,  rope,  cable, 
or  endless  chain  is  used,  it 
passes  over  two  pulleys,  as 


Fig.  53.     Transmission  of  power  by  belt. 


figure 


Jn 


(a)  the  pulleys  rotate  in  the  same  direction,  while  in  case  (6), 
where  the  belt  is  crossed,  they  rotate  in  opposite  directions. 
It  is  evident  that  if  the  circumference  (or  diameter)  of  the 
large  pulley  is  n  times  as  great  as  the  circumference  (or 
diameter)  of  the  small  pulley,  the  latter  will  turn  n  times  as 
fast  as  the  large  pulley. 

The  same  is  true  of  cogwheels,  and  since  the  teeth  on  the 
perimeters  of  two  interlocking  wheels  must  be  the  same  size, 
it  follows  that  the  number  of  cogs  on  each  wheel  is  a  measure 


TRANSMISSION   OF  POWER  49 

of  its  circumference.  The  speeds  of  two  such  wheels  are  in- 
versely proportional  to  the  number  of  teeth  on  them.  Just 
as  in  the  case  of  two  pulleys  with  a  crossed  belt,  two  cogwheels 
rotate  in  opposite  directions. 

PROBLEMS 

1.  If  it  takes  22  pounds  to  pull  a  200-pound  sled  along  a  level  road 
covered  with  snow,  how  much  work  is  done  in  dragging  the  sled  50  feet  ? 

2.  In  the  preceding  problem,  if  the  sled  is  drawn  at  the  rate  of 
4  miles  an  hour,  how  many  horse  power  are  required  ? 

3.  How  much  work  can  a  5-horse-power  engine  do  in  10  minutes  ? 

4.  Which  does  more  work  in  a  week,  a  500-horse-power  engine  that 
runs  8  hours  a  day,   or  a  200-horse-power  engine  that  runs  all  the 
time? 

*"  5.  What  is  the  horsepower  of  an  elevator  motor,  if  it  can  raise  the 
car  with  its  load,  1500  pounds  in  all,  from  the  bottom  to  the  top  of  a 
100-foot  building  in  10  seconds  ? 

6.  In  what  time  would  you  have  to  pull  a  50-pound  bucket  of  water 
up  a  well  33  feet  deep  in  order  to  be  working  at  the  rate  of  ^  horse 
power  ? 

7.  An  airplane  with  a  300-horse-power  engine  makes  60  miles  an 
hour.     What  is  the  thrust  of  the  propeller? 

8.  A  locomotive  pulling  a  train  along  a  level  track  at  the  rate  of  25 
miles  an  hour  expends  750  horse  power.     Find  the  total  resistance  over- 
come. 

9.  A  motor  has  a  4-inch  pulley  which  is  belted  to  a  16-inch  pulley 
on  an  overhead  shaft.     The  motor  is  making  1800  revolutions  per 
minute.     What  is  the  speed  of  the  overhead  shaft  ? 

10.  A  certain  air  compressor  should  run  at  240  r.  p.  m.  and  it  has  a 
50-inch  pulley.     An  electric  motor  is  available  and  runs  at  1200  r.  p.  m. 
How  large  a  pulley  should  be  fitted  to  the  motor? 

11.  In  an  electric-car  motor  a  pinion,  or  small  cogwheel,  attached  to 
the  armature  shaft  has  20  cogs,  and  the  gear  wheel  attached  to  the 
car  axle  has  36  cogs.     If  the  car  wheel  is  33  inches  in  diameter,  find  the 
number  of  revolutions   the   motor  makes  while   the   car   goes    100 
feet. 


50 


SIMPLE   MACHINES 


the  direction  of  motion  and  makes  the  two  rear 
wheels  independent. 


12.  An  automobile  with  30-inch  rear  wheels  is  going  20  miles  an 
hour.  The  gear  ratio  of  the  differential  (B  :  P  in  Fig.  54)  is  3.63.  How 
many  revolutions  per  minute  (r.  p.  m.)  is  the  engine  making? 

13.  If  the  same  en- 
gine, running  at  the  same 
speed,  is  connected  with 
the  rear  wheels  through 
a  worm  gear  which  has 
30  teeth  on  the  gear 
wheel,  what  is  the  speed 
of  the  car  in  miles  per 
hour? 

PRACTICAL  EXERCISES 

1.  The  horse  power  of 
a  man.  Measure  the 
vertical  height  of  some 

Fig.  54.  The  differential  on  an  automobile  changes  iong  flight  of  steps.  De- 
termine with  a  stop 
watch  how  long  it  takes 

you  to  run  up.     Compute  the  work  done  in  lifting  your  own  weight 

this  vertical  distance  and  from  this  get  your  horse  power.     Get  your 

friends  to  try  this  experiment. 

2.  Power  to  operate  household  machines.  Find  out  how  much  horse 
power  you  can  put  forth  while  turning  something  like  a  bread  mixer  or 
ice-cream  freezer.  (Hint.  Use  a  spring  balance  to  measure  the  pull 
required,  both  at  the  beginning  and  at  the  end  of  your  experiment, 
and  use  the  average.  Also  measure  the  radius.  Then  see  how  many 
turns  you  can  make  in  1  minute.) 

45.  Friction.  What  we  have  thus  far  said  about  machines 
has  been  on  the  assumption  that  friction  could  be  neglected. 
Often,  however,  friction  plays  a  very  important  part  in  the 
operation  of  a  machine,  sometimes  detrimentally  and  some- 
times to  our  great  advantage.  We  may,  therefore,  profitably 
inquire  what  friction  is  and  how  it  acts,  what  determines  its 
magnitude,  and  how  it  affects  what  a  machine  can  do. 

By  friction  we  mean  the  resistance  which  opposes  every  effort 
to  slide  or  roll  one  body  over  another. 


FRICTION   CLUTCHES 


51 


46.  Friction  often  a  help.  Many  machines,  devices,  and 
processes  depend  upon  friction  for  their  successful  operation. 
Without  friction  belts  would  not  cling  to  their  pulleys,  auto- 
mobile, street-car,  and  railroad  brakes  would  not  work,  ropes 
could  not  be  made,  and  nails,  screws,  and  matches  would  be 
useless.  Even  walking  would  be  impossible,  as  any  one  can 
see  who  has  tried  to  run  on  a  highly  polished  floor  or  on  ice. 

No  railroad  train  or  automobile  could  move  without  friction, 
because  it  is  the  traction,  or  friction,  between  the  driving  wheels 
and  the  rail  or  road  that  pushes 
them  forward.  It  is  to  increase  the 
traction  that  the  surfaces  of  auto- 
mobile tires  are  often  made  with 
knobs  or  irregular  projections  that 
bite  into  soft  roads,  or  with  little 
suction  cups  or  cavities  that  tend  to 
stick  to  smooth  pavements.  On  wet  days  automobilists  also 
use  chains  (Fig.  55)  to  increase  their  traction,  and  locomotive 
drivers  sprinkle  sand  on  the  tracks  just  in 
front  of  their  wheels.  Good  traction  is 
quite  as  important  in  stopping  as  in  start- 
ing an  automobile  or  a  train.  When  auto- 
mobile wheels  slip  at  all,  they  are  likely 
to  slip  sidewise  as  well  as  forward ;  this  is 
called  skidding.  It  is  dangerous  because 
the  automobile  is  temporarily  quite  out  of 
control.  To  avoid  it,  drive  slowly  around 
corners  or  through  sand,  and  use  chains  in 
wet  weather. 


Fig-  55-  Chains  on  automobile 
wheels  tend  to  prevent  skid- 
ding. 


Fly  wheel 


Where 
pedal  presses 


Clutch 
spring 


Fig.    56.      Cone   clutch, 

which  joins  the  engine 

to  the  driving  shaft.  47.  Friction  clutches.  Furthermore,  auto- 

mobile engines  deliver  their  power  to  the 

driving  shaft  through  some  sort  of  friction  clutch.  In  the  cone 
clutch  (Fig.  56)  a  leather-faced  cone  is  pushed  into  the  tapered  rim  of 
the  flywheel  by  springs.  In  the  multiple  disk  clutch  (Fig.  57)  there 
is  a  series  of  metal  disks  arranged  in  two  groups.  Every  other  disk 


52 


SIMPLE   MACHINES 


Disks  attached 
to  shaft    . 


Release 
Pedal 


is  a  driving  disk  that  turns  with  the  flywheel ;  the  alternate,  or  driven, 
disks  are  attached  to  the  main  shaft.     When  the  driving  and  driven 

disks  are  pressed  to- 
gether by  the  clutch 
springs,  the  driving 
disks  drag  the  others 
Driving  around  with  them. 
We  see,  then,  that  in 
both  cases  the  power 
is  transmitted  en- 
tirely through  fric- 
tion contacts.  When 
the  driver  wants  to 
stop  the  car,  he  re- 
leases the  clutch  by 


Shaft 


Fig.  57.  Multiple  disk  clutch.  Every  other  disk  is 
joined  to  the  engine;  the  rest  are  joined  to  the 
driving  shaft. 


pushing  a  foot  pedal. 
This  takes  off  the 
thrust  of  the  clutch 
springs  and  lets  the  disks  separate,  so  that  the  driving  disks  can 
rotate  independently  of  the  driven  disks.  The  cone  clutch  releases 
in  a  similar  manner. 

48.  Factors  affecting  friction.     The  factors  which  determine 
the  amount  of  friction  in  any  particular  case  are  so  numerous 
and  uncertain  that  only  the  most  general  principles  can  be  stated 
positively.     In  general,   friction  depends  on  velocity,   on  the 
nature  and  condition  of  the  rubbing  surfaces,  and  on  the  load. 

49.  Effect  of  velocity  on  friction.     It  is  commonly  said  that 
friction  does  not  depend    much   on   velocity,   and   this   is  ap- 
proximately true.     Nevertheless,  starting  friction  is  distinctly 
greater  than  sliding  friction,  as  anyone  can  see  who  pulls  a 
box  or  heavy  block  of  wood  across  a  table  top  with  a  spring 
balance.     This  is  why  a  locomotive  can  start  a  heavy  train 
if  the  driving  wheels  are  not  allowed  to  slip ;   whereas  if  they 
slip  at  all,  they  spin  rapidly  without  doing  much  good.    Further- 
more,   friction    usually    decreases    somewhat    with    increasing 
speed;  thus  the  friction  between  the  brake  shoes  and  the  wheels 
of  railroad  cars  is  only  one  third  to  one  half  as  great  at  60 
miles  an  hour  as  at  20  miles  an  hour.     This  is  why  an  engineer 


EFFECT  OF  SURFACES  ON  FRICTION  53 

or  motorman  lessens  the  pressure  of  his  brakes  as  his  train  or 
car  slows  down. 

60.  Effect  of  surfaces  on  friction :  lubrication.  On  the  other 
hand,  friction  depends  very  much  on  the  nature  and  condition 
of  the  rubbing  surfaces.  Friction  is  less  when  the  surfaces  are 
smooth  and  hard.  Thus  two  well-finished  metal  surfaces  may 
show  only  about  half  as  much  friction  as  two  wooden  surfaces 
under  the  same  conditions,  and  these  only  about  half  that  of 
two  unpolished  stone  surfaces. 

Friction  is  also  much  diminished  by  proper  lubrication.  Soap  or 
paraffin  rubbed  on  a  bureau  drawer  that  sticks  may  make  it  much  easier 
to  move.  Two  well-oiled  or  greased  metal  surfaces  may  show  only 
•J-  or  even  ^  as  much  friction  as  the  same  surfaces  when  dry.  This 
is  why  it  is  so  important  to  attend  to  the  lubrication  of  all  sorts  of 
machines,  not  only  the  large  machines  in  shops,  but  also  sewing  ma- 
chines, bicycles,  windmills,  agricultural  machinery,  farm  engines,  and 
particularly  automobiles.  People  seem  to  forget  that  an  automobile 
should  be  supplied  with  oil  and  grease  just  as  faithfully  and  regularly 
as  with  gasoline.  If  this  is  not  done,  the  increased  friction  in  the  va- 
rious bearings  and  in  the  cylinders  makes  them  wear  much  faster. 
Sooner  or  later,  also,  a  bearing  "  burns  out."  This  means  that  the 
surface  of  the  bearing,  which  is  made  of  a  whitish,  easily  melted  metal 
called  Babbitt  metal,  melts  or  tears  out,  leaving  a  rough  surface  and  a 
very  loose  fit.  Then  the  engine  "  knocks,"  and  the  shocks  may  break 
a  connecting  rod  and  wreck  everything.  Or  sometimes  a  bearing  or  a 
piston  may  "  freeze,"  which  means  that  the  shaft  or  piston  has  ex- 
panded with  the  heat  until  it  has  stuck  fast  and  stopped  the  machine. 
"  Hot  boxes  "  on  railroads  are  familiar  examples  of  what  happens  when 
something  goes  wrong  with  lubrication. 

Not  only  should  every  machine  get  frequent  lubrication  but  each 
part  should  have  the  right  kind  of  lubricant.  Thus,  automobile  wheel 
bearings  need  grease,  the  differential  needs  a  heavy  semi-solid  oil  mix- 
ture, the  crank  case  a  suitable  grade  of  cylinder  oil,  and  the  leaves  of 
the  springs  an  oil  and  graphite  paste.  A  watch  bearing,  on  the  other 
hand,  needs  the  best  grade  of  light  pure  sperm  oil.  Detailed  direc- 
tions about  lubrication  are  supplied  with  all  valuable  machines,  and 
these  directions  should  be  scrupulously  followed. 

51.  With  dry  surfaces  friction  does  not  depend  much  on  the 
of  contact.     That  is,  it  takes  about  the  same  pull  to  drag 


800  g. 


54  SIMPLE  MACHINES 

a  brick-shaped  block  across  a  table  top  when  the  block  is 
standing  on  end,  as  when  it  is  lying  on  its  side.  On  the  other 
hand,  with  well-lubricated  surfaces  friction  is  nearly  proportional 
to  the  area  of  contact. 

62.  Effect  of  load  on  friction :  coefficient  of  friction.  When 
a  box  is  loaded,  it  requires  much  more  force  to  pull  it  along 
than  when  it  is  empty.  In  fact,  the  force  needed  to  slide  a 
given  box  over  a  certain  floor  is  just  about  doubled  when  the 
total  weight  of  the  box  and  its  contents  is  doubled,  and  tripled 
when  the  weight  is  tripled.  In  many  cases  the  rubbing  sur- 
faces are  not  horizontal  and  the  force  pushing  them  together 

is  not  a  weight;    but  here 
also  the  backward  drag  due 
to  friction  doubles  or  triples 
.  whenever   one    doubles    or 
triples    the    perpendicular 
force  with  which  the  rub- 
g(W(7  ,/V       bing  surfaces  press  against 
CEsS^    each  other.     In  general,  the 

Fig.  58.    Determining  the  coefficient  of  force  needed  to  overcome  fric- 
fnction.  faon  js  neariy  proportional  to 

the  total  normal  pressure;  that  is,  the  fraction  —  friction  divided 
by  total  normal  pressure  —  is  nearly  constant  for  a  given  pair 
of  surfaces,  no  matter  what  the  load.  This  fraction  is  called 

the  coefficient  of  friction. 

_  force  of  friction 

Coefficient  of  friction  = 

total  normal  pressure 

FOR  EXAMPLE,  suppose  a  block  weighing  800  grams  is  dragged  slowly 
along  a  horizontal  board  by  a  force  of  300  grams,  as  shown  in  figure  58. 
Then  the  coefficient  of  friction  is  fif$>  or  0.375. 

Often  the  coefficient  of  friction  that  applies  to  a  given  case 
is  at  least  approximately  known  from  engineering  handbooks 
or  previous  experience.     Then  the  force  of  friction  can  be  com- 
puted by  means  of  the  equation, 
Force  of  friction  =  coefficient  of  friction  X  total  normal  pressure. 


EFFICIENCY  OF  MACHINES  55 

FOR  EXAMPLE,  if  the  weight  carried  by  the  driving  wheels  of  a  certain 
locomotive  is  160,000  pounds,  and  the  coefficient  of  friction  between  the 
wheels  and  the  track  is  known  to  be  about  0.25,  the  maximum  pull 
which  the  locomotive  can  exert  before  its  wheels  slip  is  0.25  X  160,000, 
or  40,000  pounds. 

53.  Efficiency  of  machines.  In  the  first  part  of  this  chapter 
we  assumed  that  we  were  dealing  with  ideal  or  perfect  ma- 
chines, where  friction  plays  no  part.  In  such  cases  the  output 
equals  the  input  of  work.  But  in  every  actual  machine  friction 
causes  a  loss  or  waste  of  work.  It  takes  some  input  of  work 
merely  to  keep  the  machine  moving,  even  when  its  useful 
output  is  zero.  The  useful  work  done  by  a  machine  is  con- 
sequently always  less  than  the  work  put  into  it,  and  the  prin- 
ciple of  work  may  be  stated  in  the  form, 

Output  =  input  —  work  lost  by  friction. 

The  ratio  of  the  output  of  a  machine  to  its  input  is  called  the 
efficiency  of  the  machine.  It  is  always  less  than  one.  and  is 
usually  expressed  as  a  percentage ;  that  is,  the  output  is  a  cer- 
tain percentage  of  the  input  delivered  to  the  machine.  Output 
and  input  may  be  expressed  in  work  units  or  in  power  units. 

output        work  done  by  machine 

Efficiency  =  -—£ —  =  — J- — — , 

input         work  done  on  machine 

or  Output  =  efficiency  X  input. 

FOR  EXAMPLE,  with  a  certain  block  and  tackle  it  is  found  that  a  force 
of  125  pounds  is  necessary  to  lift  a  weight  of  500  pounds,  and  the  force 
must  move  6  feet  in  order  to  raise  the  weight  1  foot.  What  is  the  ef- 
ficiency of  this  block  and  tackle  ? 

The  output  =  1  X  500  =  500  ft.  Ibs.  and 
the  input     =  6  X  125  =  750  ft.  Ibs. 

Therefore  the  efficiency  is  %%%,  or  0.667,  or  66.7%. 

The  efficiency  of  a  lever  where  the  friction  is  very  small  is  nearly 
100%,  but  in  the  commercial  block  and  tackle  it  is  sometimes  less  than 
50%,  and  in  the  jackscrew  the  friction  is  so  large  that  the  efficiency  is 
often  as  low  as  25%. 


56  SIMPLE  MACHINES 

Friction  in  machines  can  be  diminished,  and  efficiency  in- 
creased, by  using  ball  or  roller  bearings.  The  chief  objection  to 
them  is  their  high  cost. 

PROBLEMS 

1.  A  tool  is  pressed  on  a  grindstone  with  a  force  of  25  pounds  ;  the 
coefficient  of  friction  is  0.3.     What  is  the  backward  pull  of  friction  ? 

2.  The  coefficient  of  friction  between  the  driving  wheels  of  a  loco- 
motive and  the  rails  is  0.25.     How  much  weight  must  be  carried  on  the 
driving  wheels  if  the  locomotive  is  to  exert  a  pull  of  15  tons  ? 

3.  A  test  shows  that  it  takes  a  force  of  17  pounds  to  pull  on  ice  a 
man  weighing  150  pounds.     What  is  the  coefficient  of  friction? 

4.  In  lifting  a  1250-pound  block  of  marble  to  a  height  of  90  feet,  the 
hoisting  engine  did  125,000  foot  pounds  of  work.     What  was  the  effi- 
ciency of  the  hoist  ? 

6.  What  load  can  a  pair  of  horses,  working  at  the  rate  of  2  horse 
power,  draw  along  a  level  highway  at  the  rate  of  3  miles  an  hour,  if 
the  coefficient  of  friction  between  the  sled  runners  and  the  ice-covered 
road  is  0.02  ? 

6.  It  takes  a  pull  of  150  pounds  to  haul  a  load  of  one  ton  up  an  in- 
clined plane  which  rises  5  feet  in  100  feet  along  the  incline.     What  is 
the  efficiency  ? 

7.  A  motor  whose  efficiency  is  90%  delivers  5  horse  power.   What 
must  be  the  input  ? 

8.  What  is  the  efficiency  of  a  pump  which  can  deliver  250  cubic  feet 
of  water  per  minute  to  a  height  of  20  feet,  if  it  takes  a  10-horse-power 
engine  to  run  it  ? 

9.  A  centrifugal  pump  is  designed  to  deliver  50,000  gallons  of  water 
per  minute  at  a  height  of  10  feet,  and  has  an  efficiency  of  70%.     What 
should  be  the  horse  power  of  the  steam  turbine  chosen  to  drive  it? 

10.  A  steam  shovel  driven  by  a  6-horse-power  engine  lifts  200  tons 
of  gravel  to  a  height  of  15  feet  in  an  hour.     How  much  work  is  done 
against  friction  ? 

11.  A  builder's  jackscrew  (Fig.  52)  is  used  to  lift  10  tons.     There 
are  5  threads  to  the  inch  and  the  radius  of  the  effort-arm  is  2  feet.     The 
efficiency  of  the  screw  is  40%.     How  great  a  pull  is  required  ? 

12.  If  a  400-horse-power  hoisting  engine  can  pull  a  ton  of  ore  up  a 
mine  shaft  a  mile  deep  in  1  minute,  what  is  the  efficiency  of  the  ma- 
chinery ? 


SUMMARY  f  57 

SUMMARY  OF  PRINCIPLES  IN  CHAPTER  II 

The  principle  of  moments — used  in  solving  all  kinds  of  levers, 
straight  and  bent,  the  wheel  and  axle,  etc. : 

Effort  X  its  lever  arm  =  resistance  X  its  lever  arm. 
To  get  force  on  fulcrum  or  to  solve  a  pulley  system, 
Sum  of  forces  up  =  sum  of  forces  down. 

resistance  effort  distance 

Mechanical  advantage  =  — — = :  . 

effort  resistance  distance 

Laws  of  equilibrium,  applicable  to  any  object  at  rest  under  the 
action  of  two  or  more  forces : 

(1)  Sum  of  forces  in  any  direction 

=  sum  of  forces  in  opposite  direction. 

(2)  Sum  of  moments  clockwise  around  any  point 

=  sum  of   moments  counterclockwise    around  same 
point. 

The  principle  of  work : 

Work  (foot  pounds)  =  force  (pounds)  X  distance  (feet). 
In  any  frictionless  machine, 

Output  =  input. 
If  there  is  friction, 

Output  =  input  —  work  lost  by  friction. 
Power  =  rate  of  doing  work. 

1  horse  power  =  550  foot  pounds  per  second, 

=  33,000  foot  pounds  per  minute. 

_  force  of  friction 

Coefficient  of  fnction  = 

total  normal  pressure 

Force  of  friction  =  coefficient  X  total  normal  pressure. 

output       work  done  by  machine 

Efficiencv  = =  ; T~. —  • 

input        work  done  on  machine 

Output  =  efficiency  X  input. 


SIMPLE  MACHINES 


Fig.  59.    Ball  bearings  used  in  a  bicycle. 


QUESTIONS 

1.   Make  a  list  of  a  dozen  applications  (not  mentioned  in  this  book) 
of  the  simple  machine  elements  described  in  this  chapter  that  you  have 

seen  outside  of  the  classroom 
within  a  week.  Make  a  simple 
sketch  of  each. 

2.  Distinguish  between  the 
popular  use  of  the  term  "  work  " 
and  its  technical  use  in  physics 
and  engineering.  Give  an  ex- 
ample of  "  work  "  that  is  not 
technically  "  work." 

3.  What  simple  machine  elements  do  you  find  in  the  following 
machines :  clothes  wringer,  broom,  ice-cream  freezer,  plow,  grindstone, 
and  rotary  meat  chopper. 

4.  Distinguish     b  e- 
tween      the      terms 
"  mechanical     advan- 
tage" and  "efficiency." 
Illustrate   by    an    ex- 
ample. 

6.  Is  there  any  me- 
chanical advantage  in 
an  equal-arm  lever  ? 
Why  is  it  often  used  in 
machines  ?  Why  is  an 
unequal-arm  lever  use- 
ful? 

6.  Figure  59  shows 
the  way  in  which  ball 
bearings  are  used  in  a 

bicycle  pedal.    Explain  how  this  device  diminishes  friction, 
are  roller  bearings  used  in  an  automobile  ? 

7.  Show  how  the  principle  of  work  applies  to  the  lever. 

8.  Figure  60  shows  the  construction  of  the  ordinary  platform  scales. 
Notice  that  it  is  merely  a  combination  of  levers.    Identify  the  fulcrum 
of  each  lever.     Explain  why  the  load  to  be  weighed  may  be  placed 
anywhere  on  the  platform. 


Fig.  60. 


Platform  scales  illustrating  a  combina- 
tion of  levers. 


Where 


QUESTIONS 


59 


9.   Why  are  you  apt  to  twist  off  the  head  of  a  small  screw  by  using 
a  screwdriver  in  a  bit  brace? 

10.  When  a  machinist  speaks 
of  "an  8-32  screw,"  what  does 
he  mean  ? 

11.  What      determines     the 
"  angle  of  repose,"  or   slope,  of 
the  rock  waste,  or  talus,  at  the 
base  of  a  cliff  ? 

12.  Why  are  the  modern  air 
brakes    on    cars  more  effective 
than     the    old-fashioned    hand 
brakes  ? 


13.  Why  can  a  pair  of  horses 
draw  a  heavier  load  along  a 
hard,  smooth  road  than  over 
a  muddy  or  sandy  road?  (Look 
up  rolling  friction.) 


Fig.  60  A.    Computing  scales. 


14.  Why  is  it  better  in  stopping  a  train  or  an  automobile  not  to 
apply  the  brakes  so  hard  that  the  driving  wheels  are  held  fast  and 
merely  slide? 


PRACTICAL  EXERCISES 

1.  Efficiency  of  automobile  jacks.    To  get  a  load  of  several  hundred 
pounds,  place  a  long  timber  (perhaps  8  feet  long  and  2  by  4  inches) 
across  the  jack.     Put  a  weight  of  50  pounds  on  one  end  of  the  timber 
and  place  the  jack  at  a  short  distance  (1  to  2  feet)  from  the  other  end, 
which  is  fastened  down.     Measure  the  effort  required  to  lift  the  load. 
Compute  the  efficiency  of  the  jack  under  several  loads. 

2.  Computing  scales.    Describe  the  construction  of  the  computing 
scales  shown  in  figure  60  A,  which  are  often  found  in  grocers'  shops 
and  meat  markets.    Explain  how  they  work. 


CHAPTER  III 
MECHANICS  OF  LIQUIDS 

Machines  using  liquids  —  force  and  pressure  —  pressure  in 
a  liquid  due  to  its  weight  —  levels  of  liquids  in  connecting 
vessels  —  Pascal's  principle  of  transmitted  pressure  —  appli- 
cations in  presses  —  upward  pressure  of  liquids  —  Archimedes' 
principle  and  its  applications  —  specific  gravity  of  solids  and 
liquids  —  city  waterworks,  hydrants,  faucets,  gauges,  and 
meters  —  water  wheels  —  cohesion  and  adhesion  —  capil- 
larity. 

64.  Machines  using  liquids.     Some  machines  involve  more 
than  the  levers,  pulleys,  screws,  gears,  and  other  simple  elements 
that  we  studied  in  Chapter  II.     For  instance,  water  wheels, 
hydraulic  presses,  and  hydraulic  jacks  make  use  of  liquids. 
Furthermore,   ships  float,   anchors  sink,   and   submarines   do 
either  at   the  will   of   their   commanders,  in   accordance  with 
certain  laws  that  deal  with  liquids. 

Finally  we  shall  learn  how  certain  principles  of  the  mechanics 
of  liquids  are  involved  in  the  operation  of  city  fire  departments, 
waterworks,  and  sewage  systems. 

65.  Force  and  pressure.     In  studying  liquids  we  must  dis- 
tinguish carefully  between  force  and  pressure.     Force  means 
a  push  or  pull.    Forces  are  usually  expressed  in  pounds  or  grams 
or  kilograms.     Pressure  means  the  push  or  pull  per  unit  area 
of  the  surface  acted  upon.     That  is, 

force 

Pressure  =  , 

area 

Force  =  pressure  X  area. 

Pressures  are  usually  expressed  in  pounds  per  square  inch,  or  in 
grams  per  square  centimeter. 

60 


DOWNWARD  PRESSURE  IN   VESSELS 


61 


66.  Pressure  in  a  liquid  due  to  its  weight.  Water  standing 
in  a  cylindrical  open-topped  tank  (Fig.  61)  exerts  a  force  on 
the  bottom  of  the  tank  because  the  water  is  heavy.  The  total 
force  against  the  bottom  is  the  total  weight  of  the  water.  The 
pressure  is  the  weight  of  so  much  of  the 
water  as  rests  on  one  square  foot  or  one 
square  centimeter  of  the  bottom.  This 
water  can  be  thought  of  as  forming  a 
little  column  extending  from  the  bottom 
of  the  tank  to  the  surface  of  the  water, 
and  with  a  cross  section  of  just  one 
square  foot  or  one  square  centimeter. 
The  volume  of  this  column  is  numerically 
equal  to  its  height,  that  is,  to  the  depth 


of  the   water;    and   the  weight  of   the  Fig.6i.    Cylindrical  water 
column  is  its  volume  times  its  density ;      staves™'16  °f  redwood 
this  weight  is  the  pressure  at  the  bottom. 
Evidently  for  liquids  in  open  tanks  or  vessels, 

Pressure  =  depth  X  density, 
Total  force  =  area  X  depth  X  density. 

FOB  EXAMPLE,  suppose  we  have  a  box  the  bottom  of  which  is  10  cen- 
timeters by  20  centimeters,  and  which  is  15  centimeters  deep. 

If  the  box  is  full  of  water,  each  square  centimeter  of  the  bottom  sup- 
ports a  column  of  water  15  centimeters  tall,  weighing  15  grams,  and  the 
pressure  on  the  bottom  is  15  grams  per  square  centimeter.  The  total 
downward  force  on  the  bottom  would  be  200  X  15  X  1,  or  3000  grams. 

If  the  box  is  filled  with  mercury  instead  of  water,  each  square  cen- 
timeter supports  a  column  of  mercury  the  volume  of  which  is,  as  before, 
15  cubic  centimeters.  But  since  one  cubic  centimeter  of  mercury 
weighs  13.6  grams,  this  column  weighs  15  X  13.6  =  204  grams,  and  the 
pressure  is  204  grams  per  cubic  centimeter.  The  total  force  on  the 
bottom  would  be  200  X  15  X  13.6  grams,  or  40.8  kilograms. 

57.  Downward  pressure  in  differently  shaped  vessels.  So 
far  we  have  considered  vessels  with  vertical  sides.  In  the 
ordinary  pail,  however,  the  sides  are  not  vertical,  but  flare 


62  MECHANICS  OF  LIQUIDS 

outward  as  in  case  B  in  figure  62.  Perhaps  one  might  expect 
that  the  pressure  on  each  square  centimeter  of  the  bottom 
would  be  greater  than  in  case  A,  because  there  is  so  much 
more  water  in  the  vessel.  This,  however,  is  not  true.  Each 
square  centimeter  of  the  bottom  has  to  hold  up  only  the  little 
column  of  water  above  it,  just  as  it  did  in  case  A.  The  extra 
water  above  the  slanting  sides  is  held  up  by  those  sides  and 


Fig.  62.     Vessels  with  variously  shaped  sides.     A,  vertical ;   B,  flaring ; 

C,  conical. 

not  by  the  bottom.  If  the  area  of  the  base  and  the  depth  of 
liquid  are  the  same'  in  A  and  B,  the  total  downward  push  of 
the  liquid  on  the  bottom  will  be  the  same,  even  though  B  holds 
more  liquid  than  A. 

In  case  C  the  depth  of  liquid  and  area  of  base  are  the  same 
as  in  cases  A  and  B,  but  the  top  is  smaller  than  the  base.  It 
is  easy  to  see  that  the  pressure  on  that  portion  of  the  base  ab 
directly  under  the  top  would  be  the  same  as  in  the  other  ves- 
sels, but  it  might  at  first  seem  that  the  pressure  would  gradually 
decrease  as  we  go  from  a  to  c  and  from  b  to  d.  But  this  is 
not  true.  Just  as,  when  the  sides  slope  outward,  they  hold 
up  the  excess  of  water,  so,  when  they  slope  inward,  they  push 
down  enough  to  make  up  for  the  deficit  in  water.  In  all  three 
cases  in  figure  62,  the  pressure  and  total  force  on  the  bottom 
are  the  same;  that  is,  the  downward  pressure  of  a  liquid  is 
independent  of  the  shape  of  the  vessel. 

Figure  63  shows  an  ingenious  apparatus  similar  to  that  invented 
by  Pascal  in  France  to  illustrate  these  principles.  A  vessel  of  any 
desired  shape  screws  into  a  base  ring  carrying  a  thin,  corrugated  metal 
disk  that  serves  as  the  bottom  of  the  vessel.  When  water  in  the  vessel 


UPWARD  PRESSURE  OF  LIQUIDS 


63 


exerts  a  pressure  on  this  disk,  the  center  of  the  disk  deflects  slightly  like 

a  spring  and  turns  the  pointer  on  the  dial  by  means  of  a  rack  and 

pinion.     We  have  thus  a  sort  of  spring 

balance  for  measuring  the  pressure  on 

the  bottom  of  the  vessel.     The  tank  T, 

which  can  be  raised  and  lowered,  and 

the  flexible  connecting  tube  afford  an 

easy  means  of  filling  and  emptying  the 

vessel  C. 

By  using  vessels  of  different  shapes 
on  this  apparatus,  we  can  show  that 
when  the  depth  is  the  same  the  pressure 
on  the  bottom  is  also  the  same,  no 
matter  what  the  shape  of  the  vessel. 
Furthermore,  by  filling  a  vessel  slowly, 
we  can  show  that  the  pressure  increases 
proportionally  to  the  depth.  And  fi- 
nally, by  using  a  saturated  solution  of 
common  salt,  which  is  denser  than 
water,  we  can  show  that  at  the  same 
depth  the  bottom  pressure  is  propor- 
tional to  the  density. 


Fig.  63.  Pressure  on  bottom  is 
independent  of  the  shape  of  the 
vessel.  (Pascal's  vases.) 


58.  Upward  pressure  of  liquids.  If  one  tries  to  push  a  pail 
under  water  bottom  downward,  one  finds  that  considerable 
resistance  must  be  overcome  because  of  the  upward  push  of 

the  water  on  the  bottom  of  the  pail. 

To  see  just  how  much   this  upward 

push  of  the  water  is,  let  us  try  the 

following  experiment. 

As  shown  in  figure  64,  close  with  a  glass 
plate  or  piece  of  cardboard,  held  in  place 
by  a  thread,  a  glass  cylinder  which  has  its 
bottom  edge  ground  off  smooth.  When 
we  push  this  cylinder  into  a  jar  of  water, 
we  may  let  go  the  thread,  and  yet  the  glass 
bottom  will  not  fall  off.  It  is  evident  that 
there  is  an  upward  pressure  due  to  the 
water.  If  we  slo,!,  pour  colored  water 
downward.  into  the  cylinder,  the  plate  stays  in 


'p^ 


64 


MECHANICS  OF  LIQUIDS 


place  until  the  levels  inside  and  outside  are  the  same;  then  it  falls 
off. 

In  general,  the  upward  pressure  exerted  by  a  liquid  at  any 
depth  is  equal  to  the  downward  pressure  which  would  be  exerted 
by  the  same  liquid  at  the  same  depth. 

69.  Liquids  also  exert  pressure  sidewise.  We  all  know 
that  if  a  hole  is  bored  in  the  side  of  a  tank  or  barrel  of  water, 
the  water  will  spurt  out.  This  means  that  before  the  hole 
was  bored  the  liquid  must  have  been  pressing  against  that  bit 
of  the  side  of  the  barrel.  Liquids,  then,  exert  a  sidewise  pres- 
sure due  to  their  weight,  as  well  as  a  downward  pressure. 

We  can  investigate  how  this  sidewise  pressure  varies  with  the  depth 
by  means  of  the  gauge  shown  in  figure  65.  It  consists  of  a  rubber  dia- 
phragm D,  which  may  be  turned  about  a 
horizontal  axis,  and  is  connected  by  a  rub- 
ber tube  to  a  horizontal  glass  tube  contain- 
ing a  globule  B  of  some  colored  liquid.  As 
we  lower  the  pressure  gauge  into  the  jar  of 
water,  we  observe  that  the  globule  moves 
to  the  right,  showing  a  gradual  increase 
of  pressure  with  increase  of  depth.  If  we 
repeat  this  with  the  diaphragm  facing  in 
another  direction,  we  get  the  same  result. 
If  we  hold  the  frame  at  some  fixed  depth, 
and  rotate  the  diaphragm  around  a  hori- 
zontal axis,  we  find  that  the  globule  remains 
practically  stationary,  showing  that  the 
pressure  is  the  same  in  all  directions. 

The  sidewise  pressure  of  a  liquid  in- 
creases with  the  depth  and  density  of  the 
liquid.  At  a  given  depth  a  liquid  exerts 
in  all  directions  exactly  the  same  pressure. 
60.  Calculation  of  sidewise  force.  To  calculate  the  total 
push  of  water  against  a  dike  or  dam,  we  have  to  remember 
that  the  sidewise  pressure  increases  gradually  from  zero  at  the 
surface  to  its  maximum  value  at  the  bottom.  We  have  already 
seen  that  at  the  bottom  the  pressure  is  equal  to  the  weight 


Fig.  65.  Pressure  gauge 
shows  that  pressure  in  a 
liquid  is  equal  in  all  di- 
rections. 


LEVELS  OF  LIQUIDS  IN  CONNECTING  VESSELS     65 


15'  cm 


of  a  column  of  water  with  a  base  one  unit  square  and  with  a 
height  equal  to  the  depth.  The  average  sidewise  pressure 
is  equal  to  the  pressure  halfway  down,  or  one  half  the  bottom 
pressure.  And,  as  always, 

Force  =  area  X  average  pressure. 

FOR  EXAMPLE,  suppose  we  have  a  box  10  centimeters  wide,  20  centi- 
meters long,  and  15  centimeters  deep  filled  with  water  (Fig.  66). 
What  is  the  total  force  tending  to 
push  out  the  end  of  the  box  ?  The 
pressure  at  a  point  halfway  down 
the  side  would  be  7.5  grams  per 
square  centimeter.  There  are  in 
the  end  10  X  15,  or  150  square 
centimeters.  Therefore  the  total 
force  against  the  end  is  150  X  7.5, 
or  1125  grams. 

Again,  suppose  the  box  were  a 
large  tank  Ml  of  water,  and  the   •*,£, 
dimensions,  expressed  in  feet,  were       times  average  pressure. 
10  by  20  by  15.     What  is  the  end 

thrust  ?  The  pressure  halfway  down  would  be  the  weight  of  a  column 
of  water  with  1  square  foot  for  its  base  and  7.5  feet  high,  namely, 
7.5  X  62.4,  or  468  pounds  per  square  foot.  Since  there  are  10  X  15, 

or  150  square  feet  in  the  end  of  the 
tank,  the  total  end  thrust  is  150  X  468, 
or  70,200  pounds,  or  about  35  tons. 

61.  Levels  of  liquids  in  connect- 
ing vessels.  Probably  everyone  has 
observed  that  water  stands  at  the 
same  level  in  the  spout  of  a  tea- 
kettle as  in  the  kettle  itself  (Fig. 
67).  That  is,  liquids  seek  their 


any  number  of  connecting  vessels 
will  have  its  free  surface  at  the  same  level  in  each.  This 
is  to  be  expected  from  the  fact  that  the  pressure  in  a  liquid 
depends  upon  the  depth  below  the  free  surface.  Thus  if  any 


66 


MECHANICS  OF  LIQUIDS 


Fig.  68.     Water  gauge  on 
a  boiler. 


point  in  the  connecting  portion  between 
the  two  vessels  were  unequally  far  below 
the  two  surfaces,  the  pressures  in  either 
direction  would  not  balance,  and  the 
liquid  would  flow  from  one  vessel  to  the 
other  until  the  levels  were  equalized. 

The  water  gauge  on  a  steam  boiler  (Fig.  68) 
is  a  good  application  of  this  principle.  The 
gauge  consists  of  a  thick-walled  glass  tube 
which  connects  at  the  top  with  the  steam 
space,  and  at  the  bottom  with  the  water  in 
the  boiler.  The  valves  A  and  B  are  closed 
when  the  glass  tube  is  to  be  replaced.  The 
valve  C  is  opened  occasionally  to  blow  out  the 
connecting  passage,  which  sometimes  clogs  up. 


PROBLEMS 

1.  The  water  in  a  standpipe  is  10  meters  deep.    What  is  the  pres- 
sure (g./cm.2)  on  the  bottom? 

2.  The  water  in  a  standpipe  is  40  feet  deep.    What  is  the  pressure 
(Ibs./sq.  in.)  on  the  bottom? 

3.  If  the  diameter  of  the  tank  in  problem  2  is  10  feet,  what  is  the 
total  force  in  tons  which  the  bottom  of  the  tank  must 

sustain  ? 

4.  A  diver  goes  down  into  sea  water  (density 
1.03  grams  per  cubic  centimeter)  to  a  depth  of  10 
meters.     What  is  the  pressure  on  him  in  kilograms 
per  square  centimeter  ? 

6.  The  hydraulic  engineer  speaks  of  pressure  as 
"  head  of  water,"  which  means  the  pressure  due  to 
the  weight  of  a  column  of  water  as  high  as  the  "head 
of  water."  Express  in  pounds  per  square  inch  a 
"head  of  50 feet." 

6.  What  is  the  pressure,  near   the  keel,  on  a 
vessel  drawing  6  meters  in  sea  water? 

7.  Figure  69  is  a  cylindrical  can  10  X  12  centi- 
meters ;  out  of  the  top  rises  a  tube  20  centimeters  long  and  1  square 
centimeter  in  cross  section.     The  box  and  tube  are  filled  with  water. 


«— 12  cm.  — > 

Fig.  69.  Cylindri- 
cal can  and  tube 
full  of  water. 


PRESSURE   TRANSMITTED  BY  A   LIQUID  67 

(a)  Find  the  pressure  (grams  per  square  centimeter)  on  the  bottom 
of  the  tank.  Find  the  total  force  on  the  bottom. 

(6)    Does  the  size  of  the  tube  affect  the  pressure  on  the  bottom? 

(c)  Find  the  pressure  halfway  up  the  side  of  the  can.    Find  the  total 
force  against  the  cylindrical  surface  of  the  can. 

(d)  Find  the  pressure  at  the  top  of  the  can.     Find  the  total  upward 
force  against  the  top. 

(e)  What  is  the  total  weight  of  water  in  can  and  tube? 

(/)  If  the  can  and  tube  when  empty  weigh  250  grams,  how  much 
force  will  be  required  to  support  the  can  and  tube  when  they  are  filled 
with  water?  (Compare  this  answer  with  the  answers  to  part  (a)). 

8.  A  rectangular  tank  is  10  feet  long,  5  feet  wide,  and  4  feet  deep. 
Calculate  the  total  force  exerted  on  the  end  when  the  tank  is  full  of 
water. 

9.  A  cubic  inch  of  mercury  weighs  0.49  pounds,     (a)   Find  the 
pressure  on  the  bottom  of  a  tumbler  in  which  the  mercury  stands  4 
inches  deep.     (6)  If  the  tumbler  is  2  inches  in  diameter,  what  is  the 
total  force  on  the  bottom? 

10.  How  high  a  column  of  water  could  be  supported  by  a  pressure 
of  1  kilogram  per  square  centimeter  ? 

11.  The  density  of  mercury  is  13.6  grams  per  cubic  centimeter. 
What  is  the  pressure  exerted  at  the  base  of  a  column  76  centimeters 
high? 

12.  A  dam  is  50  feet  long  and  6  feet  high,  and  the  water  just  reaches 
the  top.     What  is  the  total  force  against  the  dam  ? 

13.  A  hole  6  inches  square  is  cut  in  the  bottom  of  a  boat  drawing 
10  feet  in  fresh  water.     What  force  must  be  exerted  in  order  to  hold  a 
board  tightly  against  the  inside  of  the  hole  ? 

14.  How  much  "  head  of  water  "  is  needed  to  give  a  pressure  of  1 
pound  per  square  inch? 

15.  What  must  be  the  difference  in  height  between  a  fire  hydrant 
and  the  surface  of  the  water  in  a  city  reservoir  to  give  a  pressure  of  50 
pounds  per  square  inch  at  the  hydrant? 

16.  The  bottom  of  a  tin  pail  is  16  centimeters  in  diameter  and  the 
top  is  24  centimeters  in  diameter.     Suppose  the  pail  is  filled  with  water 
to  a  depth  of  25  centimeters,     (a)  What  is  the  pressure  on  the  bot- 
tom?    (6)  What  is  the  whole  force  on  the  bottom? 

62.  Pressure  transmitted  by  a  liquid.  Thus  far  we  have 
been  considering  the  pressure  at  various  depths  below  the 


68 


MECHANICS  OF  LIQUIDS 


surface  of  a  liquid  in  an  open  vessel, 
case  of  a  completely  confined  liquid. 


Let  us  take  now  the 


Fig.  70. 
fitted 


Box  filled  with  water  and 
with  three  equal  pistons. 


FOR  EXAMPLE,  the  box  in  figure  70 
is  completely  filled  with  water  and  is 
fitted  with  two  equal  pistons  A  and 
B.  Any  external  force  exerted  on  A 
will  be  transmitted  by  the  water  un- 
diminished  to  B.  If  there  is  a  third 
equal  piston  C  in  the  side  of  the  box, 
the  same  force  will  be  transmitted 
undiminished  to  C,  in  addition  to 
the  push  on  C  which  is  due  to  its 
depth. 


Any  external  force  exerted  on  a  unit  area  of  a  confined  liquid 
is  transmitted  undiminished  to  every  unit  area  of  the  interior 
of  the  containing  vessel.  This 
fact  was  first  stated  by 
the  French  mathematician, 
Pascal  (Fig.  71). 

63.  The  hydraulic  press. 
The  most  useful  application 
of  this  principle  can  be 
described  in  Pascal's  own 
words :  "  If  a  vessel  full  of 
water,  closed  in  all  parts, 
has  two  openings,  of  which 
the  one  is  a  hundred  times 
the  other,  placing  in  each  a 
piston  which  fits  it,  the  man 
pushing  the  small  piston  will 
equal  the  force  of  a  hundred 

men    who    push    that    which     Fig.  71.     Blaise  Pascal  (1623-1662).     Fa- 
is  a  hundred  times  as  large,     mous  F"nch  scientist  and  mathematician. 

and  surpass  that  of  ninety-nine.     Whatever  proportion  these 
openings  have,  and  whatever   direction  the  pistons  have,  if 


APPLICATIONS  OF   THE  HYDRAULIC  PRESS 


69 


100  Ibs. 


1  Ib. 


the  forces  that  apply  on  the  pistons  are  as  the  openings,  they 
will  be  in  equilibrium." 

Suppose  there  is  a  force  of  1  pound  pushing  down  on  the  small 
piston  (Fig.  72),  and  that  the  large  piston  has  100  times  as  great  an  area. 
It  will  be  seen  that  the  pres- 
sure on  the  large  piston  is  1 
pound  on  each  square  inch,  Sq"in. 
just  as  on  the  small  piston. 
Then  there  must  be  100 
pounds  pushing  down  on  the 
large  piston  to  balance  it. 

In  other  words,  the  pres- 


100 


Diagram  of  hydraulic  press.   Forces 
vary  as  areas  of  pistons. 


sure  is   transmitted  by   the  Fig>  ?2 

liquid  so  as  to  act  with  the 

same  force  on  every  square  inch,  and  the  forces  exerted  on  the  two 

pistons  are  directly  as  their  areas. 

64.  Applications  of  the  hydraulic  press.     This  device  of  Pascal  gives 

us  an  easy  way  of  exerting  enormous  forces,   such  as  are  needed 

in  pressing  books  into  shape 
in  book-binderies,  in  baling 
paper  and  cotton,  in  press- 
ing sheet  steel  into  shape 
for  automobile  mud  guards, 
in  extracting  oil  out  of  seeds, 
etc.  The  commercial  ma- 
chine (Fig.  73)  is  exactly  like 
that  described  by  Pascal 
except  that  there  is  usually 
a  check  valve  v  between  the 
small  piston  and  the  big 
one,  and  the  small  piston 
is  arranged  to  work  like  a 
pump,  with  a  valve  d  at  the 
bottom  for  admitting  more 
oil.  Often  the  small  piston 
is  forced  down  by  a  lever. 


Fig.  73.     Cross  section  of  a  hydraulic  press. 


The  method  of  operation  is  simple.  On  the  upstroke  of  the  pump 
piston,  the  valve  at  the  bottom  of  the  pump  opens,  and  oil  flows  in 
from  the  reservoir.  On  the  downstroke  of  the  pump  piston,  the  oil 
is  forced  over  through  the  connecting  pipe  past  the  valve,  and  pushes 
the  large  working  piston  up  very  slightly.  If  the  large  piston  is  100 


70 


MECHANICS  OF  LIQUIDS 


times  as  large  in  cross  section  as  the  small  piston  (diameters  as  10 : 1), 
the  large  piston  is  lifted  only  y^o" tne  distance  the  pump  piston  is  pushed 
down  at  each  stroke.  But  since  the  force  exerted  by  the  large  piston  is, 
if  we  neglect  friction,  100  times  that  applied  to  the  small  piston,  it 
follows  that  the  work  done  on  the  machine  is  equal  to  the  work  done  by 
the  machine.  In  the  actual  case  the  output  is  less  than  the  input  by 
the  amount  of  work  done  against  friction. 

Pascal's  principle  is  also  used  in  the  hydraulic  elevators  which  are 
commonly  employed  in  buildings  where  heavy  loads  are  to  be  lifted. 

H 


Fig.  74.     Hydraulic  chair  with  cross  section  of  base. 

The  hydraulic  jack  is  a  very  compact  machine  for  lifting  heavy 
weights,  from  50  to  600  tons,  through  short  distances  up  to  1  foot. 
Perhaps  the  most  familiar  use  of  this  principle  is  found  in  the  hydrau- 
lic chair  used  by  dentists  and  barbers  (Fig.  74).  Explain  its  working. 

PROBLEMS 

1.  If  the  diameters  of  two  pistons  in  a  hydraulic  press  are  1  inch  and 
10  inches,  what  are  their  areas  of  cross  section? 

2.  If  the  small  piston  in  problem  1  is  subjected  to  a  pressure  of  10 
pounds  per  square  inch,  what  pressure  must  be  applied  to  the  large 
piston  to  hold  it  in  place?     Neglect  friction. 

3.  If  a  total  force  of  10  pounds  is  applied  to  the  small  piston  in  prob- 
lem 1,  what  total  force  must  be  applied  to  the  large  piston  to  hold  it  in 
place? 


BUOYANT  EFFECT  OF  LIQUIDS 


71 


4.  The  diameters  of  the  pistons  in  a  hydraulic  press  are  20  inches 
and  1  inch.    What  must  be  the  force  on  the  small  piston  if  a  forte 
of  5  tons  is  to  be  exerted  by  the  large 

piston  ? 

5.  In   problem  4,  suppose  the  small 
piston  to  move  1  foot.     How  far  does  the 
large  piston  move? 

6.  The  water  pressure  in  a  city  water 
main  is  50  pounds  per  square  Inch  and 
the  diameter  of  the  plunger  of  an  elevator 
is    10   inches.      (a)  Neglecting   friction, 
compute  how  heavy  a  load  the  elevator 
can  lift?     (6)  If  the  friction  loss  is  25%, 
what  load  can  be  lifted  ? 

7.  In  the  little  working  model  of  a 


Fig.  75.     Working  model  of  a 


hydraulic  press  shown  in  figure  75,  the  hydraulic  press, 

large  piston  is  1  inch  in  diameter  and  the  small  piston  is  0.25  inches 
in  diameter.  The  small  piston  is  worked  by  a  lever  and  is  attached  at 
a  point  2  inches  from  the  fulcrum.  If  a  force  of 
20  pounds  is  applied  at  a  point  10  inches  from  the 
fulcrum,  what  force  is  exerted  by  the  large  piston  ? 

8.  A  man  weighing  150  pounds  stands  on  the 
upper  board  C  of  a  hydrostatic  bellows  (Fig.  76) 
and  pours  water  into  the  tube  to  lift  his  own  weight. 
If  the  board  is  1  foot  square,  how  high  will  the 
water  stand  in  the  tube  above  that  in  the  bellows  to 
balance  his  weight  ? 

PRACTICAL  EXERCISES 


Fig.  76.  The  man 
lifts  his  own 
weight  by  pour- 
ing in  water. 


1.  Construction  of  dams.    Study  the  cross  section 
of  some  large  dams  and  explain  the  shape.     Why  are 
some  dams  curved  with  the  convex  side  upstream  ? 

2.  Construction    of    water   tanks.     What  is  the 
^ method  used  to  get  greater  strength  at  the  bottom  ? 

65.  Buoyant  effect  of  liquids.  When  we  are  swimming, 
our  bodies  are  very  nearly  floated  by  the  water.  When  we 
lift  a  stone  from  the  stream  bed,  we  find  that  it  becomes  heavier 
on  emerging  from  the  water.  Things  seem  to  be  lighter  under 
water;  in  other  words,  water  buoys  up  anything  placed  in  it: 


72 


MECHANICS  OF  LIQUIDS 


In  order  to  find  how  much  lighter  an  object  is  under  water 
than  it  is  out  of  water,  let  us  try  the  following  experiment. 

We  have  a  hollow  metal  cylindrical  cup  C,  and  a  cylindrical  block 
B,  which  has  been  nicely  turned  to  fit  inside  the  cup   C.      We  hang 

both  from  a  beam  balance,  as 
shown  in  figure  77,  and  coun- 
terbalance with  a  weight  W 
on  the  other  scalepan.  Then 
we  bring  a  glass  of  water  up 
under  the  block  B,  so  that 
it  is  entirely  under  water. 
The  left-hand  side  of  the  bal- 
ances rises,  which  shows  the 
upward  push  of  the  water 
upon  B.  But  we  can  restore 
the  equilibrium  again  by 
pouring  water  into  the  cup  C 
until  it  is  just  filled.  This 
shows  that  B  loses  in  apparent 
weight  the  weight  of  its  own 
bulk  of  water.  If  we  try  the 
experiment,  using  kerosene 
Fig.  77.  Buoyant  effect  of  liquids  is  equal  to  instead  of  water,  we  find  that 
weight  of  liquid  displaced.  exaetly  the  same  thing  ig  tnje> 

66.  Archimedes'  principle.  The  principle  proved  by  this 
experiment  may  be  stated  as  follows  : 

The  loss  of  weight  of  a  body  submerged  in  a  liquid  is  the  weight 
of  the  displaced  liquid. 

It  is  supposed  that  this  principle  about  the  loss  of  weight 
of  a  body  in  a  liquid  was  discovered  about  250  B.C.  by  the 
old  Greek  philosopher  Archimedes.  Hiero,  king  of  Syracuse, 
suspected  a  goldsmith  who  had  made  a  crown  for  him,  and 
ordered  Archimedes  to  find  out  if  any  silver  had  been  mixed 
with  the  gold  in  the  crown.  To  do  this  without  destroying 
the  crown  seemed  a  puzzle  at  first,  but  one  day,  while  Archi- 
medes was  in  the  public  bath,  he  noticed  that  his  body  was 
buoyed  up  by  the  water  in  which  it  was  submerged.  See- 
ing in  this  effect  the  solution  of  his  problem,  he  leaped  from  the 


FLOATING  BODIES 


73 


bath  and  rushed  home  shouting,   "  Eureka !    Eureka !  "     (I 
have  found  it !    I  have  found  it !) 

67.  Explanation  of  Archimedes'  principle.    This  principle 
will  be  readily  understood  from  the  following  example. 

Suppose  we  place  a  rectangular  block  in  a  jar  of  water,  as  shown  in 
figure  78.  Let  the  block  be  10  X  6  X  4  centimeters,  and  let  the  top 
be  5  centimeters  below  the  surface  of  the 
water,  and  the  bottom  15  centimeters  be- 
neath the  surface.  Then  the  pressure  on 
top,  that  is,  the  downward  push  on  each 
square  centimeter,  is  5  grams,  and  the 
pressure  on  the  bottom,  that  is,  the  up- 
ward push  on  each  square  centimeter,  is 
15  grams.  Since  the  top  and  bottom  each 
have  an  area  of  6  X  4,  or  24  square  centi- 
meters, the  whole  upward  push  on  the 
bottom  is  24  X  15,  or  360  grams,  while  the 
whole  downward  push  on  the  top  is  only 
24  X  5,  or  120  grams.  This  leaves  a  net 
upward  force,  or  buoyancy,  of  240  grams. 


But  this  is  exactly  the  weight  of  the  dis-  Fig.  78.  Lifting  effect  of  water 
placed  water,  for  the  volume  of  the  dis-         on  submerged  block, 
placed  water  is  10  X  6  X  4  =  240  cubic  centimeters,  and  we  have  seen 
in  section  12  that  this  amount  of  water  weighs  240  grams. 

The  same  sort  of  reasoning  would  hold  at  any  depth  and 
for  any  liquid  other  than  water  and  with  any  irregularly  shaped 
body.  So  it  may  be  said  that  in  any  liquid  of  any  density 
a  body  seems  lighter  by  the  weight  of  the  displaced  volume 
of  that  liquid. 

68.  Floating  bodies.  What  happens  when  this  upward  force, 
or  buoyant  force,  is  more  than  the  weight  of  the  body  sub- 
merged? Evidently  the  body  rises  and  continues  to  rise  as 
long  as  the  upward  push  remains  greater  than  the  downward 
pull  of  gravity.  But  as  soon  as  any  of  the  body  projects 
above  the  surface,  less  water  is  displaced  and  the  upward 
push  is  less.  When  enough  of  the  body  projects  to  reduce 
the  buoyant  force  to  equality  with  the  weight,  the  body  stops 


74  MECHANICS  OF  LIQUIDS 

rising  and  floats.     In  this  case  we  see  that  the  loss  of  weight 
is  the  whole  weight  itself. 

A  floating  body  displaces  its  own  weight  of  the  liquid  in  which 
it  is  floating. 

The  following  experiment  will  help  to  make  this  principle  of  Archi- 
medes, as  applied  to  floating  bodies,  seem  more  real.  Suppose  we  bal- 
ance an  overflow  can  on  a  platform  scale,  as  shown  in  figure  79.  The 
can  is  filled  to  overflowing  with  water  and  is  balanced  by  the  weights 
on  the  other  platform.  We  place  a  dish  to  catch  any  more  water  that 


Fig.  79.     Floating  body  displaces  its  own  weight  of  liquid. 

overflows,  and  then  put  a  block  of  wood  gently  into  the  can.  After  the 
water  has  stopped  overflowing,  it  will  be  seen  that  the  scales  again 
balance.  This  means  that  the  weight  of  water  which  flowed  over  was 
just  equal  to  the  weight  of  the  block.  This  can  be  verified  in  another 
way  by  weighing  the  water  displaced  by  the  block  and  caught  in  the 
dish. 

69.  Applications  of  Archimedes'  principle.  If  we  know  the  total 
weight  of  a  ship  and  its  equipment,  we  can  tell  at  once  what 
weight  of  water  it  will  displace,  and  so  it  is  possible  to  compute  how 
deep  it  must  sink  to  displace  its  own  weight  of  water.  It  is  also  evi- 
dent that  a  boat  must  sink  a  little  deeper  in  fresh  water  than  in  salt 
water,  and  will  sink  deeper  when  loaded  than  when  empty. 


APPLICATIONS  OF  ARCHIMEDES'   PRINCIPLE        75 


A  submarine  boat  (Fig.  80)  is  so  constructed  that  it  is  only  slightly 
lighter  than  water.     It  can  be  submerged  by  letting  water  into  the 


w 


Propeller- 

Air 'Tanks  Battery       'Balancing  Tanks  «»w«»   fankg 

Fig.  80.     Submarine  floats  or  is  submerged  by  varying  its  displacement. 

ballast  tanks  and  can  be  made  to  rise  again  by  forcing  compressed  air 
into  the  ballast  tanks  and  thus  driving  the  water  out  of  them. 

The  same  principle   is  applied  in  the  floating   drydock  shown  in 
figure  81.     When  the  tanks  T,  T,  T  are  full  of  water,  the  dock  sinks 
until  the  water  level  is  at  LL. 
The  ship  to   be   repaired   is 
then   floated    into    the   dock 
and  the  water  is  pumped  out 
of  the  tanks  T,  T,  T.    As  the 
compartments  are  emptied  of 
water,  the  dock  rises  until  the 
water    level    is    at    the    line 
W  W,  lifting  the  ship  out  of  Fig.  81.     Cross  section  of  floating  drydock. 
water.      The   ship   and    dry- 
dock  still  displace  their  own  weight  of  water,  but  the  displacement  is 
in  a  different  place. 

PROBLEMS 

1.  A  piece  of  stone  weighing  235  grams  in  air  and  128  grams  in  water 
is  put  into  a  dish  just  full  of  water.     How  much  water  runs  over? 

2.  A  rowboat  weighs  200  pounds.     How  many  cubic  feet  of  water 
does  it  displace? 

3.  If  a  ferryboat  weighs  800  tons,  what  volume  of  sea  water  will  it 
displace  after  it  takes  on  board  a  train  weighing  600  tons  ? 

4.  What  is  the  volume  of  a  125-pound  boy  if  he  can  float  entirely 
submerged  except  his  nose? 

6.  A  barge  is  20  feet  long  and  10  feet  wide,  and  has  vertical  sides. 
When  an  automobile  weighing  4000  pounds  is  driven  on  board,  how 
much  deeper  in  the  water  does  the  boat  sink? 


76  MECHANICS  OF  LIQUIDS 

6.  A  rectangular  block  is  22  centimeters  long,  6  centimeters  wide, 
and  4  centimeters  high,  and  floats  in  water  with  1  centimeter  of  its 
height  above  water.     How  much  does  it  weigh  ? 

7.  A  cube  5  centimeters  on  an  edge  weighs  600  grams  in  air.    How 
much  does  it  weigh  in  water? 

8.  How  much  will  a  10-centimeter  cube  of  brass  (density  8.4  grams 
per  cubic  centimeter)  weigh  in  gasoline  (density  0.75  grams  per  cubic 
centimeter)  ? 

9.  A  rectangular  solid   10  X  8  X  6  centimeters  is  submerged  in 
water  so  that  the  top,  whose  dimensions  are  10  X  8  centimeters,  is 
horizontal  and  12  centimeters  below  the  water  surface. 

(a)  Find  the  total  force  pressing  down  on  the  top. 

(6)  Find  the  total  force  pushing  up  on  the  bottom. 

(c)  Find  the  loss  of  weight  of  the  solid. 

10.  A  river  barge  60  feet  long  and  20  feet  wide  floats  5  feet  out  of 
water  when  empty.  It  is  loaded  with  coal  until  the  top  of  the  barge 
is  only  1  foot  out  of  water.  How  many  long  tons  (2240  Ibs.)  of  coal 
were  in  the  load  ? 

PRACTICAL  EXERCISES 

1.  Floating  docks  and  bridges.  How  are  the  pontoons  constructed  ? 
How  are  they  anchored  ?  What  determines  how  much  they  can  carry  ? 

,2.  Life  preserver.  How  much  effort  is  required  to  keep  the  average 
person  afloat  in  fresh  water?  Why  does  this  depend  on  how  much  of 
the  body  is  kept  under  water?  Determine  the  lifting  effect  of  a 
standard  life  preserver  when  entirely  submerged.  What  part  of  an 
average  person's  body  would  be  kept  above  water  by  a  standard  life 
preserver?  (See  Packard's  Everyday  Physics,  Ginn  &  Co.) 

70.  Specific  gravity  and  density.  Archimedes'  principle 
furnishes  us  with  a  convenient  method  of  comparing  the  weight 
of  a  substance  with  the  weight  of  an  equal  bulk  of  water.  The 
ratio  of  these  weights  is  called  the  specific  gravity  of  the  body. 
In  other  words, 

weight  of  body 


Specific  gravity  = 


weight  of  equal  bulk  of  water 


FOR  EXAMPLE,  a  piece  of  marble  weighs  100  grams  and  an  equal  bulk 
of  water  weighs  40  grams ;  then  the  marble  is  100/40  =  2.5  times  as 
heavy  as  the  water.  The  specific  gravity  of  marble,  then,  is  2.5. 


DETERMINING  SPECIFIC  GRAVITY  OF  SOLIDS       77 

The  term  specific  gravity  does  not  mean  quite  the  same 
thing  as  density.  The  specific  gravity  of  a  substance  is  an 
abstract  number;  for  example,  the  specific  gravity  of  mercury 
is  13.6.  But  the  density  of  a  substance  is  a  concrete  number; 
for  example,  the  density  of  mercury  is  13.6  grams  per  cubic 
centimeter,  or  850  pounds  per  cubic  foot. 

In  the  metric  system  the  density  of  water  is  one  gram  per 
cubic  centimeter,  and  therefore 

Density  (g.  per  cm.3)  =  (numerically)  specific  gravity. 

In  the  English  system  the  density  of  water  is  62.4  pounds 
per  cubic  foot,  and  therefore 

Density  (Ibs.  per  cu.  ft.)  =  (numerically)  62.4  X  specific  gravity. 

71.   Methods   of    determining    specific   gravity   of    solids. 

GENERAL  RULE.  First  weigh  the  object.  Next  find  by 
some  indirect  method  the  weight  of  an  equal  bulk  of  water.  Finally 
divide  the  weight  of  the  object  by  the  weight  of  the  equal  bulk  of 
water. 

This  general  statement  covers  all  the  various  processes 
for  finding  the  specific  gravity  either  of  solids  or  of  liquids. 
The  different  procedures  vary  only  in  the  method  of  finding 
the  weight  of  an  equal  bulk  of  water. 

1st  Method.  If  the  object  is  a  regular  geometrical  solid,  one 
can  measure  its  dimensions  and  calculate  its  volume,  and  from 
that  get  the  weight  of  an  equal  bulk  of  water. 

2d  Method.  If  the  object  is  a  solid  that  will  sink  in  water 
and  will  not  dissolve,  one  can  determine  its  apparent  loss  of 
weight  in  water.  This  is  the  weight  of  an  equal  bulk  of  water. 
That  is, 

weight  of  body 
Specific  grav,ty  =  loss  of  weight  in  water 

FOR  EXAMPLE,  suppose  a  piece  of  copper  weighs  178  grams  in  air  and 
158  grams  in  water.  The  loss,  20  grams,  is  the  weight  of  an  equal  bulk 
of  water.  Therefore  the  specific  gravity  of  copper  =  178/20  =  8.9. 


78 


MECHANICS  OF  LIQUIDS 


Fig.  82 

gravity 


3d  Method.  If  the  object  is  lighter  than 
water  and  does  not  dissolve,  select  a  suf- 
ficiently large  sinker  and  suspend  it  below 
the  object,  as  shown  in  figure  82.  Then 
bring  a  jar  of  water  up  under  the  whole 
thing  until  the  water  level  is  between  the 
sinker  and  the  object,  and  weigh.  Then 
raise  the  jar  still  farther  until  the  water 
level  is  above  the  object,  and  weigh  again. 
This  weight  will  be  less  than  the  first  because 
in  this  case  the  water  buoys  up  the  object, 
while  in  the  first  case  it  does  not.  The  dif- 
.  Specific  ference  between  the  two  weights  is  equal  to 
with  sinker.  the  weight  of  the  water  displaced  by  the  object. 

0       .A  weight  of  body 

Specific  gravity  = * . 

lifting  effect  of  water  on  body  only 

FOR  EXAMPLE,  suppose  a  piece  of  wood  weighs  120  grams  in  air,  and 
that  the  wood  and  a  suitable  sinker  weigh  270  grams  when  the  sinker  is 
under  water,  and  90  grams  when  both  are  under  water.  Then  the  lift- 
ing effect  of  the  water  on  the  wood  is  270—90,  or  180  grams.  There- 
fore the  specific  gravity  of  the  wood  is  120/180  =  0.667. 

Notice  that  the  loss  of  weight,  or  the  lifting  effect  of  the  water, 
is  larger  than  the  whole  weight.  This  is  why  the  body  floats. 

72.   Specific  gravity  of  liquids. 

1st  Method.  Weigh  a  bottle  empty,  then  full  of  the  liquid, 
and  then  full  of  water.  Subtract  the  weight  of  the  empty 
bottle  in  each  case,  and  then  compare  the  weight  of  the  liquid 
with  the  weight  of  an  equal  volume  of  water. 


Specific  gravity  = 


weight  of  liquid 

weight  of  equal  volume  of  water 


FOR  EXAMPLE,  a  bottle  weighs  400  grams  when  empty  and  perfectly 
dry,  900  grams  when  full  of  water,  and  775  grams  when  full  of  gasoline. 
Then  the  specific  gravity  of  gasoline  is  |-J-§.  =  0.75. 


SPECIFIC  GRAVITY  OF  LIQUIDS 


79 


Bottles,  called  specific-gravity  flasks  (Fig. 
83),  are  made  for  the  purpose  of  determining 
the  specific  gravity  of  liquids  with  great  accu- 
racy and  facility.  They  are  usually  made  to 
contain  a  definite  quantity  of  pure  water  at 
a  specified  temperature,  such  as  500  grams, 
when  filled  to  a  mark  on  the  neck. 

2d  Method.  Weigh  a  piece  of  glass  in  air, 
then  in  the  liquid,  and  then  in  water.  Find 
the  loss  of  weight  in  the  liquid  and  the  loss 
of  weight  in  water.  This  loss  of  weight  in  the 
liquid  is  the  weight  of  the  liquid  displaced,  and 
the  loss  of  weight  in  water  is  the  weight  of  an 
equal  volume  of  water.  Then 

loss  of  weight  in  liquid 


Fig.  83.   Specific- 
gravity  flask. 


Specific  gravity 


loss  of  weight  in  water 


FOR  EXAMPLE,  suppose  the  glass  weighs  330  grams  in  air,  150  grams  in 
sulfuric  acid,  and  230  grams  in  water.     The  glass  loses  180  grams  in 
acid  and  100  grams  in  water.      Since  these  are  the 
weights  of  equal  volumes  of  acid  and  water,  the  specific 
gravity  of  the  acid  =  180/100  =  1.8. 

3d  Method*  The  most  common  way  of  de- 
termining the  specific  gravity  of  liquids  is  by  the 
hydrometer.  This  is  usually  made  of  glass,  and 
consists  of  a  cylindrical  stem  and  a  bulb  weighted 
with  mercury  or  shot  to  make  it  float  upright 
(Fig.  84).  The  liquid  is  poured  into  a  tall  jar, 
and  the  hydrometer  is  gently  lowered  into  the 
liquid  until  it  floats  freely.  The  point  where 
the  surface  of  the  liquid  touches  the  stem  of 
the  hydrometer  is  noted.  There  is  usually  a 
paper  scale  inside  the  stem,  so  made  that  the 

*  There  is  another  method,  using  balancing  columns,  which  will  be  de- 
scribed in  the  Laboratory  Manual.  To  understand  it  one  must  have  read 
Chapter  IV. 


Fig.  84.  Hy- 
drometer used 
to  measure 
specific  grav- 
ity of  liquids. 


80 


MECHANICS  OF  LIQUIDS 


noo 


specific  gravity  (or  density  in  grams  per  cubic  centimeter)  can 
be  read  off  directly.  In  light  liquids,  like  kerosene,  gasoline, 
and  alcohol,  the  hydrometer  must  sink  deeper  to  displace  its 
weight  of  liquid  than  in  heavy  liquids  like  brine,  milk,  and  acids. 
In  fact,  it  is  usual  to  have  two  separate  instruments,  one  for 
heavy  liquids,  on  which  the  mark  1.000  for  water  is  near  the 
top,  and  one  for  light  liquids,  on  which  the  mark  1.000  is  near 
the  bottom  of  the  stem. 

73.  Commercial  uses  of  the  hydrometer.  Since  the  commercial 
value  of  many  liquids,  such  as  sugar  solutions,  sulfuric  acid,  al- 
cohol, and  the  like,  depends  directly  on 
the  specific  gravity,  there  is  extensive  use 
for  hydrometers.  Perhaps  the  best-known 
form  of  hydrometer  is  the  land  used  in  test- 
ing milk,  called  a  lactometer.  The  specific 
gravity  of  cow's  milk  varies  from  1.027  to 
1.035.  Since  only  the  last  two  figures  are 
important,  the  scale  of  a  lactometer  is  made 
to  run  from  20  to  40,  which  means  from 
1.020  to  1.040.  The  specific  gravity  of 
milk  does  not  give  a  conclusive  test  as  to 
its  worth.  In  addition  to  water  (which  is 
about  87%),  milk  contains  some  substances 
which  are  heavier  than  water,  such  as  al- 
bumin, sugar,  and  salt;  and  others  that 
are  lighter  than  water,  such  as  butter  fat. 
Besides  the  specific  gravity,  one  needs  to 
determine  the  amount  of  fat,  and,  if  pos- 
sible, of  the  other  solids  in  the  milk,  in 
order  to  know  its  richness.  Of  course  the 
most  important  question  about  milk  is  its 


1200 


Fig.  85.  Syringe  hydrometer 
used  to  test  storage  bat- 
teries. 


cleanness,  but  this  must  be  left  to  the  bacteriologist. 

Another  very  common  use  of  the  hydrometer  is  in  testing  the  ordi- 
nary lead-plate  storage  battery.  In  section  326  we  shall  learn  that  the 
liquid  in  this  battery  is  dilute  sulfuric  acid,  and  that  the  condition  of  the 
battery  as  to  charge  and  discharge  is  best  determined  by  measuring  the 
density  of  this  acid.  When  the  battery  is  fully  charged,  the  solution 
should  have  a  specific  gravity  of  about  1.29,  and  as  the  battery  dis- 
charges the  specific  gravity  drops  to  about  1.15.  In  testing  the  auto- 
mobile storage  battery,  the  hydrometer  is  made  small  and  inclosed  in  a 


QUESTIONS  AND   PROBLEMS  81 

large  glass  tube  (Fig.  85).  To  get  a  sample  of  the  acid,  the  bulb  at  the 
top  of  the  large  glass  tube  is  squeezed  and  then  released,  thus  drawing 
up  liquid  enough  to  float  the  hydrometer. 

QUESTIONS  AND  PROBLEMS 

1.  A  piece  of  ore  weighs  42  grams  in  air  and  25  grams  in  water. 
Calculate  its  specific  gravity. 

2.  A  stone  weighs  15  pounds  in  air  and  9  pounds  in  water, 
(a)    Find  its  specific  gravity. 

(6)    Find  its  density  in  the  metric  system, 
(c)    Find  its  density  in  the  English  system. 

3.  A  body  has  a  specific  gravity  of  3.5.     What  is  its  density  in 
(a)  the  metric  system,  and  (6)  the  English  system  ? 

4.  Which  has  the  greater  specific  gravity,  whole  milk  or  skim  milk  ? 
Why? 

6.   Which  has  the  greater  specific  gravity,  pure  milk  or  watered 
milk?     Why? 

6.  If  the  specific  gravity  of  lead  is  1 1 .4,  how  many  cubic  centimeters 
of  lead  does  it  take  to  make  a  kilogram  weight  ? 

7.  If  the  specific  gravity  of  cork  is  0.25,  how  many  cubic  feet  of  cork 
are  there  in  1  pound  of  cork  ? 

8.  A  block  of  wood,  15  X  10  X  8  centimeters,  floats  with  one  of  its 
largest  faces  2  centimeters  out  of  water. 

(a)    Find  its  weight. 

(6)   Find  its  specific  gravity. 

9.  A  plank  8  centimeters  thick  floats  with  5  centimeters  under 
water.     Find  its  specific  gravity. 

10.  A  boy  is  carrying  a  40-pound  pail  of  water  in  one  hand  and  a 
2-pound  trout  in  the  other.     The  specific  gravity  of  the  trout  is  1. 
He  puts  the  trout  into  the  pail  of  water,     (a)     What  is  the  "  loss  of 
weight  "  of  the  trout?     (6)  How  much  does  the  boy  have  to  lift? 

11.  A  block  of  wood  weighs  150  grams ;  a  sinker  is  suspended  from  it, 
and  when  the  sinker  is  under  water  and  the  block  is  in  air,  the  combina- 
tion weighs  350  grams.     When  the  wood  and  the  sinker  are  both  under 
water,  they  weigh  100  grams.     Find  (a)  the  volume  of  the  block  of 
wood,  and  (6)  its  specific  gravity. 

12.  If  a  boy  can  lift  a  90-pound  stone  on  dry  land,  how  heavy  a  stone 
can  he  raise  from  the  bottom  of  a  swimming  hole  ?    Assume  the  specific 
gravity  of  the  stone  to  be  2.5. 


82  MECHANICS  OF  LIQUIDS 

13.  A  cube  of  iron  10  centimeters  on  an  edge  (specific  gravity  7.5) 
floats  in  mercury  (specific  gravity  13.6).     How  many  cubic  centimeters 
are  above  the  mercury  ? 

14.  A  can  weighs  190  grams  when  empty,  600  grams  when  full  of 
water,  and  613  grams  when  full  of  milk. 

(a)    What  is  the  capacity  of  the  can  in  cubic  centimeters  ? 
(6)    What  is  the  specific  gravity  of  the  milk? 

15.  How  much  does  1  cubic  centimeter  of  lead  (specific  gravity  11.4) 
weigh  in  kerosene  (specific  gravity  0.79)  ? 

16.  A  bottle  weighs  80  grams  when  empty,  280  grams  when  filled 
with  water,  and  250  grams  when  filled  with  a  medicine.     What  is  the 
specific  gravity  of  the  medicine  ? 

17.  An  empty  bottle  weighs  50  grams  ;  the  same  bottle  full  of  water 
weighs  200  grams.     Some  dry  sand  is  put  into  the  empty  bottle  and  it 
then  weighs  320  grams.     Finally  the  bottle  is  again  filled  with  water, 
and  the  bottle,  sand,  and  water  weigh  370  grams. 

(a)   Find  the  capacity  of  the  bottle. 

(6)    Find  the  volume  of  the  sand. 

(c)    Find  the  specific  gravity  of  the  dry  sand. 

18.  If  one  buys  10  pounds  of  mercury  (specific  gravity  13.6),  how 
many  cubic  inches  should  one  get  ? 

19.  If  the  inside  of  an  ice  chest  measures  24  X  18  X  12  inches,  how 
many  pounds  of  ice  (specific  gravity  0.92)  will  it  hold  ? 

20.  How  many  pounds  of  sulfuric  acid  (specific  gravity  1.84)  does  a 
5-gallon  carboy  contain  ? 

PRACTICAL  EXERCISE 

Making  a  hydrometer.  Use  a  test  tube  with  a  one-hole  rubber 
stopper  carrying  a  thin-walled  glass  tube.  Ballast  the  test  tube  with 
lead  shot.  How  can  you  make  such  a  hydrometer  indicate  directly 
specific  gravity? 

74.  City  waterworks.  Every  city  has  to  face  the  problem 
of  providing  a  plentiful  supply  of  pure  water  for  household 
use,  for  industrial  purposes,  and  for  fire  protection.  Not 
only  must  there  be  enough  water,  but  it  must  be  furnished 
at  sufficient  pressure  to  force  it  to  the  tops  of  high  buildings. 
If  the  city  is  located  near  the  mountains,  as  are  Denver  and 
Los  Angeles,  it  is  an  easy  matter  to  conduct  the  water  from 


FAUCETS  AND  HYDRANTS 


83 


an  elevated  reservoir  in  large  pipes  or  mains  to  the  houses. 
Since  the  water  tends  to  seek  its  own  level,  it  will  rise  in  the 


Fig.  86.     Cross  section  of  a  water  system. 

buildings  to  the  height  of  the  reservoir.  But  in  most  cities, 
such  as  New  York,  Philadelphia,  and  Boston,  the  gravity 
system  of  waterworks  is  impossible  and  a  pumping  system  must 
be  employed.  This  includes  an  extensive  watershed  sometimes 
at  a  long  distance  from  the  city,  a  holding  reservoir,  aqueducts, 
pumping  stations,  standpipes,  and  distributing  mains  (Fig.  86). 
The  operation  of  the  big  steam  pumps  that  are  used  will  be 
explained  later  (section  194). 

75.  Faucets  and  hydrants.  The  only  parts  of  this  great  system  of 
water  pipes  which  we  ordinarily  see  are  the  fire  hydrants  on  the  edges 
of  our  sidewalks,  and  the  taps  or  faucets  at  our  sinks  and  bathtubs. 
Each  is  merely  a  valve  for  opening  and  closing  a  pipe. 

The  internal  construction  of  the  ordinary 
faucet  is  shown  in  figure  87.  The  handle  oper- 
ates a  screw  which  forces  a  disk,  faced  with  a 
fiber  washer,  against  a  circular  opening,  or  seat, 
and  so  shuts  off  the  water.  If  the  handle  is 
turned  the  other  way,  the  disk  is  raised,  leaving 
an  opening.  This  sort  of  valve  may  get  out  of 
order  in  two  ways  :  the  washer  may  wear  out 
or  the  packing  about  the  handle  rod  may  get 
loose.  Both  can  easily  be  replaced.  The 
packing  consists  of  cotton  twine  wrapped 
around  the  valve  stem,  and  is  held  in  place  by  what  is  called  a 
gland. 


Fig.  87.     Cross  section 
of  common  faucet. 


84 


MECHANICS  OF  LIQUIDS 


The  internal  construc- 
tion of  a  hydrant  is 
shown  in  figure  88.  The 
fire  hose  is  attached 
near  the  top  of  the  hy- 
drant. A  wrench  applied 
to  a  vertical  rod  opens 
the  cut-off  valve.  To 
prevent  water  from 
standing  in  the  hydrant 
and  freezing  in  winter, 
there  is  an  ingenious 
device  which  opens  a 
drip  valve  at  the  bottom 
whenever  the  cut-off 
valve  is  closed. 

76.  How  we  meas- 
ure water  pressure. 
Doubtless  we  have 
all  noticed  that  water 
flows  more  slowly 
from  a  faucet  on  an 

Closed  Open 

Fig.  88.     Cross  section  of  a  fire  hydrant  with  cut-   upper  •  floor    than    on 
off  valve  closed  and  open.  the  first  floor.     This  IS 

because  the  water  pressure  is  low  there.  To  measure  it,  we 
use  some  form  of  pressure  gauge.  For  small  pres- 
sures we  take  an  open  mercury  manometer,  the 
most  accurate  form  of  pressure  gauge.  It  con- 
sists of  a  U-shaped  tube  partly  filled  with  mer- 
cury, as  shown  in  figure  89. 

Suppose,  the  water  pressure  is  enough  to  balance  a 
mercury  column  4  feet  high.     How  much  is  the  pres- 
sure in  pounds  per  square  inch  ?     A  column  of  mercury 
4  feet  high  and  1  square  inch  at  the  base  would  con- 
tain 48  cubic  inches,  and  would  weigh  23.5  pounds. 
Therefore  the  pressure  of   the  water  would  be  23.5 
pounds  per  square  inch.     With  such  a  gauge  it  is  easy   F-     g        Mer- 
to  show  that  the  water  pressure  is  less  on  the  top  floor       cury  pressure 
than  in  the  basement.  gauge. 


FLUCTUATIONS  IN   WATER  PRESSURE 


85 


A  mercury  gauge  is  so  cumbersome  and  expensive  that  a 
Bourdon  spring  gauge  is  generally  used.  It  consists  of  a 
brass  tube  of  elliptical  section,  bent  into  a  nearly  complete 
ring  and  closed  at  one  end,  as  shown  in  figure  90.  The  flat- 
ter sides  of  the  tube  form 
the  inner  and  outer  sides 
of  the  ring.  The  open  end 
of  the  tube  is  connected 
with  the  pipe  through 
which  the  liquid  under 
pressure  is  admitted.  The 

"\.       ~^*^~"~""^ '"'     ^f  A 

closed  end  of  the  tube  is 

free  to  move.     Asthepres-  Fig'  9°'     Bourdon  pressure  gauge. 

sure  increases,  the  tube  tends  to  straighten  out,  moving  a 
pointer  to  which  it  is  connected  by  levers  and  small  chains. 
These  spring  gauges  have  the  scale  so  graduated  that  they 
read  directly  in  pounds  per  square  inch. 

77.  Fluctuations  in  water  pressure.    Not  only  does  one  find 
a  decrease  of  water  pressure  in  going  from  the  basement  to  the 

attic  of  a  house,  but  if 

r?  r?  r»  E« 

the  gauge  is  attached  at 
one  point  and  watched 
closely,  it  will  be  seen 
to  fluctuate  according 
as  much  or  little  water 
'^          is   being   drawn   else- 
SH^\     where  in  the  building. 


Fig.  91.     Drop  in  pressure  due  to  friction  in  pipe.         The  following  experi- 
ment   shows    the    same 

thing  on  a  smaller  scale.  The  tank  or  reservoir  R  in  figure  91  is  con- 
nected with  a  supply  pipe  A  B.  The  pressure  along  the  pipe  is  indi- 
cated by  the  height  of  the  water  in  the  tubes  C,  D,  and  E.  When 
the  pipe  is  closed  at  B,  the  level  is  the  same  in  R,  C,  D,  and  E ;  this 
is  called  the  static  condition.  But  when  the  stopper  is  removed  from  B, 
and  water  flows  out,  the  pressure  is  no  longer  the  same  at  all  points 
along  the  pipe,  but  falls  off  as  the  distance  from  the  reservoir  R 


86 


MECHANICS  OF  LIQUIDS 


increases.  This  drop  in  pressure  is  due  to  friction  against  the  walls 
of  the  pipe  through  which  the  water  has  to  run. 

From  this  experiment  we  see  that,  when  a  number  of  faucets 
are  open  and  the  water  is  flowing,  the  pressure  in  the  neighbor- 
hood becomes  small.  To  equalize  these  changes  in  water 
pressure  and  also  to  provide  some  flexibility  in  the  system, 
it  is  common  to  have  a  standpipe  in  the  water  system  nearer 
the  houses  than  the  main  reservoir.  This  also  serves  as  an 
auxiliary  reservoir  in  case  of  emergency. 

78.  A  water  meter.  It  is  now  customary  to  measure  in 
cubic  feet  or  in  gallons  the  quantity  of  water  which  is  used 

by  each  consumer.  The  water 
meter  is  located  in  the  supply 
line  and  is  usually  in  the  base- 
ment where  the  pipe  from  the 
main  enters  the  house. 

One  of  the  commonest  meters 
used  for  domestic  purposes,  the 
disk  type,  is  illustrated  in  figure  92 
with  one  side  cut  away  to  show 
the  working  parts.    In  the  bottom 
is  the  measuring  chamber,  which 
Fig.  92.     Disk  type  of  water  meter,  side  contains  a  hard-rubber  disk.    This 
cut  away.  disk  is  attached  at  the  center  to 

a  small  sphere  which   works   in 

sockets  at  the  top  and  bottom  of  the  chamber.  The  disk  just  touches 
the  sides  of  the  chamber  all  the  way  around,  and  also  just  touches  the 
conical  upper  and  lower  faces  of  the  chamber.  As  the  water  passes 
through  the  meter,  it  causes  the  disk  to  move  with  a  rotary  nodding 
motion  (nutation),  a  certain  quantity  of  water  passing  through  the 
meter  for  each  complete  nutation  of  the  disk.  The  end  of  the  spindle 
projecting  upward  from  the  disk  moves  in  a  circular  path  and  actuates 
the  gears  that  drive  the  mechanical  counter  above. 

The  dial  of  a  water  meter  is  shown  in  figure  93.  It  consists 
of  six  circles,  each  divided  into  10  divisions.  The  number 
on  the  outside  of  each  circle  indicates  the  number  of  cubic 


WATER  WHEELS 


87 


Fig.  93- 
meter, 
cu.  ft. 


Dial    of    water 
reading     94,450 


feet  for  one  complete  revolution  of  the  hand.  Thus  the  dial 
in  figure  93  indicates  94,450  cubic  feet  (the  "  one  "circle 
not  being  read).  An  official  of  the 
water  department  reads  the  meter 
periodically,  and  by  subtracting  can 
easily  compute  the  amount  of  water 
consumed  during  the  period,  and  so  fix 
the  charge  in  proportion. 

79.  Water  wheels.  Running  and 
falling  water  have  long  been  utilized  as 
a  source  of  power.  Any  community 
having  a  waterfall  or  a  rapid  in  a  near- 
by river  has  a  valuable  source  of  power. 
The  older  types  of  water  wheels  are  the  overshot,  in  which 
the  weight  of  the  water  slowly  turns  the  wheel,  and  the  un- 
dershot, in  which  the  wheel  is  let  down  into  a  swiftly  flowing 
current.  These  older  types  of  water  wheels  are  almost  as  effi- 
cient as  modern  wheels,  but  the  amount  of  power  which  even  a 
large  wheel  can  deliver  is  too  small  for  most  installations. 
The  modern  forms  of  water  wheels  are  the  Pelton  wheel  and 

the  turbine.  The 
Pelton  wheel  is 
used  when  the 
supply  of  water  is 
small  but  the  pres- 
sure, or  "  head,"  is 
great.  Frequently 
the  water  in  a  lake 
located  high  up  on 
a  mountain  is 
brought  down  in 
strong  steel  pipes 

Fig.  94-     Pelton  water  wheel  used  for  high  heads.      ^^       allowed       to 

rush  with  terrific  velocity  against  the  cup-shaped  buckets  on 
the  rim  of  the  wheel  (Fig.  94). 


88  MECHANICS  OF  LIQUIDS 

Thus,  at  Big  Creek,   California,   the  reservoir  is  about  1900  feet 
above  the  wheels,  the  water  comes  through  a  6-inch  nozzle  at  a 
speed  of  350  feet  per  second  (about  3.5  miles  per 
minute),  and  the  water  wheels  are  94  inches  in 
diameter  and  revolve  at  375  r.p.m. 

We  may  illustrate  this  type  of  wheel  by  a  little 
water  motor  (Fig.  95),  which  may  be  attached  to  an 
ordinary  kitchen  faucet  and  used  to  drive  a  small 
grinding  wheel  for  sharpening  knives,  scissors,  and 
carpenters'  tools. 

By  far  the  most  important  type  of  water 
wheel  to-day  is  the  turbine.  This  is  used 
Fig.  95.  Water  where  a  large  flow  of  water  at  a  moderate 
motor  attached  «  head  "  is  available,  as  at  Niagara  Falls  and  at 
Keokuk,  Iowa,  on  the  Mississippi  River.  The 
turbine  wheel  (Fig.  97)  is  placed  at  the  bottom  of  a  cylindrical 
well,  or  pit,  and  is  submerged  in  water  to  a  depth  equal  to  the 
height  of  the  water  supply.  The  water  is  let  into  the  wheel  case 
through  many  inlets,  or  passages,  between  shutters  A  A,  which 
are  so  curved  as  to  direct  the  water  against  the  moving  blades 
BB  of  the  wheel  in  the  most  favorable  direction  to  produce 
rotation.  When  the  water  has  done  its  work,  it  falls  from  the 
bottom  of  the  wheel  case  into  the  "  tail  race  "  below.  The 
turbine  is  mounted  on  a  vertical  shaft,  which  transmits  the 
power  to  the  electric  generator  above.  The  amount  of  water 
which  passes  through  a  turbine  is  controlled  by  rotating  the 
guide  vanes  so  as  to  increase  or  decrease  the  size  of  the  openings 
between  the  vanes. 

The  energy  expended  upon  a  water  wheel  is  the  product  of  the 
weight  of  water  which  passes  through  it  by  the  head  of  water,  or 
the  difference  in  level  between  the  reservoir  and  the  tail  race. 

FOR  EXAMPLE,  the  head  at  Niagara  is  136  feet,  and  each  turbine  can 
handle  about  22,500  cubic  feet  of  water  per  minute.  Then  the  energy 
expended  in  one  minute  upon  each  turbine  is  22,500x62.4x136,  or 
191,000,000  ft.  Ib.  That  is,  the  input  is  about  5800  horse  power.  Since 
the  output  is  5000  horse  power,  the  efficiency  is  about  86%. 


WATER   TURBINES 


89 


<f£°»^  °,°  °  o  o  oooo 


O    0000     »00o0 

'o°«,o  «  Vo  »  C0°  «*  *•  •    * 


Fig.  96.  Horizontal  section  of  a  turbine  water  wheel  at  Keokuk,  Iowa,  to 
show  stationary  and  moving  blades.  The  water  for  each  turbine  enters  at 
four  intakes,  which  converge  into  a  scroll  chamber  so  shaped  that  the  water 
strikes  every  point  on  the  circumference  of  the  wheel  with  equal  velocity. 


Generator 


35  feet  above 
tail  water  level 


Fig.  97.     Vertical  section  of  the  above  water  turbine  in  position.  Each  turbine 

is  direct-connected  with  an  electric  generator  on  a  vertical  shaft.  There  are  at 

present  fifteen  such  units,  each  with  a  capacity  of  7500  kilowatts.  The  ultimate 
installation  at  Keokuk  will  have  twice  its  present  capacity. 


90 


MECHANICS  OF  LIQUIDS 


The   efficiency   of   modern   water  wheels  (Fig.  98)  of  both 
types  is  frequently  from  80  to  90  per  cent. 


Fig.  98.     Various  sizes  of  runners  used  in  modern  water  wheels. 

QUESTIONS  AND  PROBLEMS 

1.  What  is  the  mechanical  construction  of  the  interior  of  a  self- 
closing  faucet  ? 

2.  How  would  you  detect  by  means  of  a  water  meter  a  leak  in  your 
household  plumbing  ? 

3.  How  would  you  find  the  cost  of  the  water  used  in  a  garden  hose 
for  1  hour  ? 

4.  If  a  schoolhouse  uses  1750  cubic  feet  of  water  in  one  week  and  if 
water  costs  25  cents  per  1000  gallons,  what  is  the  weekly  water  bill  ? 

6.  The  water  level  in  a  tank  on  top  of  a  building  is  100  feet  above 
the  ground.  What  is  the  pressure  in  pounds  per  square  inch  at  a  faucet 
10  feet  above  the  ground  ? 

6.  If  200  cubic  feet  of  water  flow  each  second  over  a  dam  25  feet 
high,  what  is  the  available  power?     (Compute  the  power  required  to 
lift  the  water.) 

7.  If  the  efficiency  of  the  water  wheel  used  at  the  dam  described  in 
problem  6  is  65%,  how  many  horse  power  can  it  supply? 


COHESION  AND  ADHESION  91 

8.  How  many  cubic  feet  of  water  must  be  supplied  every  second  to 
an  overshot  wheel  which  is  20  feet  in  diameter  and  delivers  40  horse 
power  at  an  efficiency  of  85%? 

9.  In  the  power  plant  of  the  city  of  Tacoma  there  is  a  turbine  which 
uses  145  cubic  feet  of  water  per  second  at  a  head  of  415  feet.     If  the 
efficiency  is  90%,  what  is  the  horse  power? 

10.  Compute  the  output  in  horse  power  of  each  of  the  Big  Creek 
water  wheels  described  on  page  88,  assuming  that  each  wheel  is  fed  by 
one  nozzle,  and  that  the  efficiency  is  80%. 

11.  The  power  plant  at  Wallis  (Switzerland)  utilizes  a  fall  of  1650 
meters  (said  to  be  the  highest  in  the  world).     The  Pelton  wheel  de- 
velops 3000  horse  power.     If  the  efficiency  is  80%,  how  many  kilo- 
grams of  water  flow  out  every  second?     (1  horse  power  =  76  kilogram- 
meters  per  second.) 

PRACTICAL  EXERCISE 

Power  and  efficiency  of  a  water  motor.  Attach  the  motor  to  a  faucet 
and  measure  the  water  pressure  while  the  motor  is  running.  Make  a 
brake  test  by  using  two  spring  balances  with  a  he&vy  cord  around  a 
pulley.  Calculate  the  horse  power  and  efficiency  under  widely  varying 
loads.  (For  details,  see  Good's  Laboratory  Projects  in  Physics.  The 
Macmillan  Co.) 

80.  Cohesion  and  adhesion.  When  a  drop  of  water  falls 
through  the  air,  it  draws  itself  into  an  almost  perfect  sphere 
(Fig.  99).  Similarly,  lead  shot  are 
made  by  letting  molten  lead  fall 
from  a  sieve  at  the  top  of  a  tower 
into  a  pool  of  water  at  the  bottom. 
In  general,  a  liquid  when  left  to 
itself  tends  to  get  into  the  shape 
which  has  the  smallest  possible  Fig.  gg.  Pictures  showing  the 

m     ,    •      ,i  P  f  formation  of  a  drop. 

surface.     That  is,  the  surface  of  a 

liquid  acts  like  a  stretched  elastic  membrane,  which  con- 
tracts whenever  it  can.  This  tendency  is  called  surface 
tension. 

Surface  tension  is  strikingly  shown  in  soap  bubbles.  It  also  explains 
why  a  somewhat  greasy  needle,  or  even  a  light  flat-bottomed  aluminum 
tea  strainer,  can  be  floated  on  water,  although  the  metal  is  much 


92  MECHANICS  OF  LIQUIDS 

denser  than  water.  Similarly,  some  kinds  of  insects  can  walk  on  the 
surface  of  water,  being  held  up  by  surface  tension. 

Surface  tension  is  explained  by  thinking  of  a  liquid  as 
composed  of  tiny  particles  (molecules)  which  attract  each 
other  strongly.  It  is  also  observed  that  there  is  a  great 
attraction  between  many  pairs  of  sub- 
stances if  they  are  brought  very  close 
together,  as  between  wood  and  glue, 
stone  and  cement,  paint  and  wood. 
When  this  attraction  is  between  particles 
of  the  same  kind,  as  in  surface  tension, 
it  is  called  cohesion,  and  when  between 
particles  of  different  kinds,  it  is  called 
adhesion. 

Fig.  ioo.    Capillary  action        81.    Capillarity.      Suppose    we   have    two 

U-tubes     (Fig-     10°)    with     their    side    tubes 
30  mm.  and  1  mm.  in  diameter.     If  we  pour 

water  colored  with  ink  into  the  first  tube,  and  mercury  into  the  second 
tube,  we  observe  that  in  each  case  the  surfaces  in  the  two  sides  of  the 
U-tube  are  not  at  the  same  level. 

The  water  wets  the  surface  of  the  glass  and  is  attracted 
by  it;  that  is,  the  adhesion  is  great.  The  mercury  does  not 
wet  the  glass,  and  the  cohesion  of  the  particles  of  mercury  for 
each  other  makes  it  appear  as  if  there  were  repulsion  between 
glass  and  mercury.  The  surface  of  the  mercury  is  convex,  and 
it  stands  at  a  lower  level  in  the  narrow  tube  than  in  the  wide 
one.  In  the  case  of  water,  each  tube  is  drawing  the  liquid 
up  into  itself  against  the  pull  of  gravity.  The  narrower  the 
tube,  the  higher  the  liquid  is  raised.  Since  these  small  tubes 
have  hairlike  dimensions,  they  are  called  capillary  tubes  (from 
Latin  capillus,  a  hair),  and  this  phenomenon  is  called  capillarity. 
It  is  in  this  way  that  liquids  rise  in  wicks,  in  blotting  paper, 
and  in  a  sponge. 

82.  Capillarity  in  soils.  After  a  heavy  rain  the  soil  in  a 
garden  or  a  plowed  field  is  full  of  moisture  to  a  considerable 


CAPILLARITY  IN  SOILS  93 

depth.  When  the  sun  shines  again,  the  moisture  close  to 
the  surface  evaporates,  but  more  water  is  brought  up  from 
below  through  the  pores  in  the  soil  by  capillarity  and  the 
evaporation  goes  on.  If,  however,  the  soil  near  the  surface 
is  loosened  or  pulverized  by  thorough  cultivation,  the  pores 
become  too  big  for  effective  capillary  action  and  surface  evapo- 
ration is  much  reduced.  Meanwhile  capillarity  continues  to 
bring  water  up  to  where  the  roots  of  the  plants  can  use  it.  Thus 
the  moisture  is  conserved  and  put  to  good  use. 

PRACTICAL  EXERCISE 

Water  rising  in  soils.  Fill  two  lamp  chimneys  with  soil.  Put  at  the 
top  of  one  chimney  about  2  inches  of  fine,  dry,  loose  soil,  and  in  the 
other  chimney  pack  the  soil  closely  together.  Set  each  chimney  in  a 
dish  of  water.  What  does  this  experiment  demonstrate?  How  is  this 
used  in  dry  farming  ? 


SUMMARY  OF  PRINCIPLES  IN  CHAPTER  m 

Pressure  =    orce.  Force  =  pressure  X  area, 

area 

For  liquids  with  a  free  surface  (weight  of  liquid  the  only  thing 

that  counts)  : 
Pressure  is 

Independent  of  direction, 

Proportional  to  depth, 

Proportional  to  density  of  liquid, 

Equal  to  weight  of  a  column  of  liquid  with  a  base  one  unit 

square  and  a  height  equal  to  the  depth. 

Average  pressure  on  a  surface  =  pressure  at  center  of  surface. 
Total  force  on  a  surface  =  area  X  average  pressure. 

For  liquids  under  pressure  (weight  of  liquid  negligible  in  com- 
parison) : 

Pressure  is  transmitted  undiminished  in  all  directions. 
Force  varies  as  area. 


94  MECHANICS  OF  LIQUIDS 

Archimedes'  principle : 

The  loss  of  weight  of  a  body  either  partly  or  wholly  submerged 

in  a  liquid  is  equal  to  the  weight  of  the  displaced  liquid. 
If  the  body  just  floats,  this  loss  of  weight  is  also  equal  to  the 

weight  of  the  body. 

Density  =  weight  of  body. 
volume  of  body 

weight  of  body 
Specific  gravity  = 


weight  of  equal  volume  of  water 

In  the  metric  system,  since  1  cu.  cm.  of  water  weighs  1  gram, 
density  (g.  per  cm.3)  =  (numerically)  specific  gravity. 

In  the  English  system,  since  1  cu.  ft.  of  water  weighs  62.4  Ibs., 
density  (Ib.  per  ft.3)  =  (numerically)  62.4  X  specific  gravity. 

To  get  specific  gravity  : 
Find  weight  of  body. 
Find  weight  of  equal  volume  of  water. 
Divide  weight  of  body  by  weight  of  equal  volume  of  water. 

To  get  weight  of  equal  volume  of  water : 

1.  Compute  volume.     Weight  of  water  =  volume  X  density 

of  water. 

2.  Loss  of  weight  of  body  when  wholly  submerged  =  weight 

of  equal  volume  of  water.     (May  have  to  use  sinker.) 

3.  Weigh  equal  volumes  of  liquid  and  of  water  in  a  bottle. 

4.  Find  loss  of  weight  of  a  solid  in  the  liquid  and  in  water. 

(May  use  either  sinker  or  float,  i.e.,  hydrometer.) 

5.  Use  balancing  columns  (see  laboratory  manual). 

To  get  horse  power  of  water  wheels  : 

weight  of  water  per  min.  (Ibs.)  X  head  (ft.)       effide 

33,000 
The  surface  of  a  liquid  tends  to  contract  and  become  as  small  as 

possible  (surface  tension). 

Liquids  are  raised  in  tubes  which  they  wet  and  are  depressed  in 
those  which  they  do  not  wet  (capillarity). 


QUESTIONS  ON  LIQUIDS  95 

QUESTIONS 

1.  What   advantages  has   the  hydraulic  press  for  testing  steam 
boilers? 

2.  What  device  is  used  to  prevent  the  oil  or  water  from  leaking  out 
around  the  pistons  of  a  hydraulic  press  ? 

3.  How  is  Archimedes  supposed  to  have  done  his  famous  experi- 
ment with  the  crown  ? 

4.  When  a  ship  passes  from  a  river,  where  the  water  is  fresh,  into 
the  ocean,  does  it  rise  or  sink  in  the  water  ? 

6.    How  could  you  determine  the  specific  gravity  of  a  solid  soluble 
in  water,  but  insoluble  in  kerosene  ? 

6.  What  is  the  water  pressure  in  your  laboratory  ? 

7.  Two  faucets  in  a  town  show  the  same  pressure  on  the  gauge  and 
are  the  same  size.     If  one  is  one  mile  from  the  reservoir,  and  the  other 
is  two  miles  away,  will  each  faucet  deliver  the  same  quantity  of  water 
per  minute  when  opened  wide? 

8.  Sometimes  when  a  faucet  is  opened,  especially  on  an  upper  floor, 
the  water  comes  with  a  rush  at  first  and  much  more  slowly  after  it  has 
been  running  a  few  seconds.     Explain. 

9.  Why  does  one  need  to  take  temperature  into  account  in  using  the 
lactometer  ? 

10.  What  metals  float  in  mercury  ? 

11.  How  can  one  pour  a  liquid  out  of  a  glass  with  the  aid  of  a  spoon 
or  glass  rod,  so  that  it  will  not  run  down  the  side  of  the  glass  ? 

12.  Explain  the  action  of  a  towel. 

13.  Explain  the  process  of  "  fire-polishing  "  the  broken  end  of  a  glass 
tube. 

14.  If  you  know  the  displacement  of  a  battleship,  how  can  you  find 
its  weight? 

16.   Why  does  one  use  snowshoes  in  walking  over  deep  snow  ? 

16.  Why  is  it  easier  for  a  swimmer  to  float  in  the  ocean  than  in  a 
river  ? 

17.  Why  should  life  preservers  be  filled  with  cork  instead  of  hay? 

18.  A  schoolboy  in  Holland  is  said  to  have  saved  his  country  from  a 
flood  by  thrusting  his  arm  into  a  hole  in  a  dike  150  centimeters  below 
the  surface  of  the  sea.     Could  a  small  boy  hold  back  the  whole  North 
Sea? 


CHAPTER  IV 

MECHANICS  OF  GASES 

Weight  of  the  air  —  vacuum  pumps  —  uses  —  atmospheric 
pressure  —  measured  by  Torricelli's  experiment  —  barometer 
—  kinds  and  uses  —  pumps  for  liquids  —  siphon  —  buoyancy 
of  air  —  balloons  and  airships  —  air  compressors  —  uses  —  com- 
pressibility of  gases  —  Boyle's  law  —  pressure  gauges  —  ab- 
sorption and  diffusion  —  molecular  theory. 

83.  Pneumatic    machines.     Just    as    hydraulic    machines 
make  use  of  the  properties  of  liquids,  so  pneumatic  machines 
make  use  of  the  properties  of  gases.     Nowadays  we  often  clean 
our  houses  with  vacuum  pumps ;   we  use  pneumatic  tires  on 
our  bicycles  and  automobiles;    we   stop   our  express  trains 
with  air  brakes ;  we  drive  the  drills  and  hammers  in  our  shops 
with  compressed  air;  and  balloons  and  airplanes  are  rapidly 
assuming  commercial  importance.     To  understand  the  opera- 
tions of  all  these  machines,  we  must  study  the  properties  of 
gases. 

THE  ATMOSPHERE 

84.  Density  of  air.    We  are  so  accustomed  to  having  air 
about  us  that  we  do  not  ordinarily  think  of  it  as  having  either 
volume  or  weight.    We  speak  of  an  "  empty  "  bottle  when  we 
really  mean  a  bottle  filled  with  air.     But  when  we  try  to  fill 
a  narrow-necked  bottle  with  a  liquid,  we  find  that  we  can 
make  the  liquid  run  in  only  as  fast  as  the  air  gets  out.     If  we 
push  a  glass  tumbler  mouth  down  into  a  pail  of  water,  the 
glass  is  not  filled  with  water,  because  it  is  filled  with  air.     Air 
occupies  space  just  as  does  any  other  fluid. 

Furthermore,   air   and   other   gases   have   weight,   although 
we  seldom  realize  this  fact. 

96 


DENSITY  OF  AIR 


97 


Fig.  xox.    Proof  that  air  has  weight. 


In  order  to  make  it  evident  that  air  has  weight,  let  us  try  the  follow- 
ing experiments.  Suppose  we  carefully  counterbalance  on  the  scales 
(Fig.  101)  a  hollow  metal 
vessel  closed  with  an  air-tight 
valve  (a  tin  can  with  a  bicycle 
valve  soldered  into  the  top 
will  serve).  If  we  then  pump 
more  air  into  the  vessel  and 
put  it  on  the  scales  again, 
we  find  that  it  has  gained  in 
weight.  If  we  repeat  the 
process,  we  find  that  it  weighs 
a  little  more  after  each  pump- 
ing. 

In  the  same  way,  if  we  take 
a  vessel  from  which  the  air 
has  already  been  exhausted, 
such  as  an  electric-light  bulb, 
carefully  counterbalance  it, 
and  then  let  the  air  in  by 
filing  off  the  tip,  we  find  that  the  scalepan  containing  the  bulb  and 
the  broken  pieces  goes  down,  showing  that  the  air  which  has  entered 
has  weight. 

Careful  experiments  show  that  under  ordinary  atmospheric 
conditions  a  liter  of  air  weighs  about  1.2  grams,  or  1  cubic 
foot  weighs  about  1.2  ounces. 

Since  gases  have  both  volume  and  weight,  we  may  express 
their  densities  in  the  usual  way,  as  so  many  grams  per  cubic 
centimeter  or  so  many  pounds  per  cubic  foot.  For  example, 
the  density  of  ordinary  air  is  about  0.0012  grams  per  cubic 
centimeter,  or  0.076  pounds  per  cubic  foot.  Many  gases  have 
densities  even  smaller  than  that  of  air.  Thus  the  density  of 
hydrogen  under  ordinary  atmospheric  conditions  is  only  about 
0.000084  grams  per  cubic  centimeter. 

PRACTICAL  EXERCISE 

Lung  capacity.  Arrange  an  apparatus  for  measuring  your  own  lung 
capacity  and  that  of  your  fellow  students.  What  is  the  normal  lung 
capacity  of  a  person  of  your  age?  Which  have  larger  lung  capacities, 


98 


MECHANICS  OF  GASES 


athletes  or  non-athletes?    Boys  or  girls?     Can  you  increase  your  lung 
capacity  by  practicing  deep  breathing  for  several  days  or  weeks? 

85.  Vacuum  pumps.  As  long  ago  as  1650  it  occurred  to  a 
German,  Otto  von  Guericke,  then  mayor  of  Magdeburg, 
that  if  air  was  a  substance,  he  could  pump  it  out  of  a  closed 
vessel  so  as  to  leave  the  vessel  really  empty,  and  that  curious 
effects  might  be  observed  in  a  space  that  contained  nothing 
at  all.  Such  a  space  is  called  a  perfect  vacuum,  and  a  space 
from  which  part  of  the  air  has  been  removed  is  called  a  partial 
vacuum.  Vacuum  pumps  were  formerly  found  only  in  physical 
laboratories,  but  now  they  are  used  so  extensively  in  vacuum 
cleaners,  in  making  incandescent  lamps  and  X-ray  bulbs,  and 
in  maintaining  a  vacuum  in  the  condensers  of  steam  engines, 
that  they  are  of  great  commercial  importance. 

A  simple  form  of  mechanical  vacuum  pump  is  shown  in  figure  102. 
It  consists  of  a  metal  cylinder  C  fitted  with  a  piston,  and  having  at  the 

lower  end  two  short  tubes  A 
and  B,  within  which  are  self- 
acting  conical  valves,  so  ar- 
ranged that  the  air  enters 
at  A  and  leaves  through  B, 
When  the  piston  is  raised, 
the  air  in  the  vessel  R, 
which  is  to  be  exhausted, 
expands  into  the  cylinder  C 
through  the  valve  A.  When 
the  piston  is  pushed  down, 
it  compresses  this  air,  clos- 
ing the  valve  A  and  opening 


Fig.  102.  A  simple  vacuum  pump  and  receiver. 


the  outlet  valve  B.  Thus  with  each  double  stroke  a  certain  fraction 
of  the  air  in  the  vessel  R  is  removed,  this  fraction  being  the  ratio  of 
the  volume  of  C  to  the  combined  volume  of  C  and  R. 

It  will  be  seen  that  even  with  a  mechanically  perfect  pump  we  never 
take  out  quite  all  the  air ;  for  by  each  stroke  we  remove  only  a  certain 
fraction  of  the  air,  and  the  remainder  expands  to  fill  the  vessel.  In 
practice,  no  pump  is  perfect,  because  of  leakage.  To  reduce  this,  it  is 
common,  in  high-vacuum  pumps,  to  cover  the  piston  and  the  valves 
with  oil,  and  in  some  forms  made  of  glass  the  piston  is  replaced  by  a 
column  of  mercury. 


APPLICATIONS  OF   THE    VACUUM  PUMP 


99 


86.  Applications  of  the  vacuum  pump.  Vacuum  cleaning  is  an 
application  of  the  "force  of  suction,"  created  by  a  vacuum,  to  the 
cleaning  of  buildings  and  their  furnishings.  In  the  portable  vacuum 
cleaner  (Fig.  103),  an  electric  motor  is  used  to  drive  a  fan  which  sucks 
in  the  dirt  through  a  nozzle  resting  on  the  sur- 
face to  be  cleaned.  The  particles  of  dirt  pass 
with  the  air  stream  through  the  fan  into  a 
bag  attached  to  the  machine  and  are  there 
strained  out,  the  air  escaping  through  the  sides 
of  the  bag.  In  many  modern  buildings  there 
is  one  large  vacuum  cleaner  in  the  basement 
to  which  suction  pipes  run  from  the  various 
rooms.  A  rubber  hose  carrying  a  cleaning 
tool,  or  nozzle,  can  be  attached  to  any  one  of 
the  suction  pipes.  In  this  type  the  dirt  is 
usually  strained  out  of  the  air  before  the  latter 
reaches  the  vacuum  pump. 

In  pumping  the  air  from  incandescent-lamp 
bulbs,  only  a  small  space  needs  to  be  exhausted, 
but  the  desired  vacuum  is  very  high.  Usually 
less  than  one-millionth  part  of  the  air  is  left 
in  the  bulb.  For  this  work  two  mechanical 
pumps  are  used  in  tandem,  one  to  take  the  air 
directly  from  the  bulb,  and  the  other  to  take 
it  from  the  cylinder  of  the  first  pump.  The 
remaining  air  is  still  further  removed  by  burn- 
ing phosphorus  or  some  other  combustible  in  the  bulb.  X-ray  tubes 
are  made  in  much  the  same  way,  except  that  the  process  must  be 
continued  longer  so  as  to  produce  a  still  higher  vacuum. 

The  pneumatic  dispatch  tubes  used  in  department  stores  for  carry- 
ing cash  and  in  some  cities  for  carrying  mail  have  a  vacuum  pump  at 
one  end.  The  articles  to  be  sent  are  placed  in  leather  cases  which  fit 
snugly  in  the  metal  tube  and  are  sucked  through  it. 

Large  vacuum  pumps  are  also  used  to  pump  out  of  steam  condensers 
such  air  as  leaks  into  them  through  the  imperfect  joints  in  the  steam 
piping,  and  also  such  air  as  enters  the  system  dissolved  in  the  water 
fed  to  the  boilers  (see  section  104).  Without  such  pumps  this  air 
would  gradually  accumulate  in  the  condenser  and  destroy  the  vacuum 
there. 

Vacuum  pumps  are  also  used  in  chemical  laboratories,  and  in 
factories  where  fruit  juices,  condensed  milk,  or  other  food  products  are 
made,  to  cause  rapid  evaporation  at  low  temperatures  (see  section  205). 


Electric 
Motor 


103-  Porta  We  vacuum 


100  MECHANICS  OF  GASES 

PROBLEMS 

1.  If  a  liter  of  air  weighs  1.2  grams,  what  is  the  total  weight  of  the 
air  in  a  room  3  meters  high,  10  meters  long,  and  8  meters  wide? 

2.  Measure  the  dimensions  of  some  large  rectangular  room  in  feet, 
and  then  calculate  the  number  of  pounds  of  air  which  it  contains. 
(Assume  that  1  cubic  foot  of  air  weighs  0.076  pounds.) 

3.  What  would  be  the  total  weight  in  tons  of  the  gas  in  the  British 
dirigible  balloon  R-34  (capacity  2,000,000  cubic  feet)  if  the  gas  were 
pure  hydrogen  f     (Assume  density  of  hydrogen  to  be  0.0053  pounds 
per  cubic  foot.) 

4.  How  much  difference  does  it  make  in  the  total  weight  of  the  gas 
in  the  R-34  if  one  tenth  of  the  hydrogen  is  replaced  by  air  through  leak- 
age and  diffusion?     (Assume  density  of  air  to  be  0.076  pounds  per 
cubic  foot.) 

5.  A  vacuum  pump  whose  cylinder  is  500  cubic  centimeters  is  used 
to  exhaust  the  air  from  a  liter  flask.     What  is  the  density  of  the  air  left 
in  the  flask  after  3  complete  strokes  ?     (Hint.  —  Find  what  fraction  of 
the  air  is  left  after  each  stroke.) 

PRACTICAL  EXERCISE 

Suction  of  a  vacuum  cleaner.  Test  with  an  open  manometer  the 
fan  suction  of  a  vacuum  cleaner.  (For  details  see  Good's  Laboratory 
Projects  in  Physics.  The  Macmillan  Co.) 

87.  Pressure  of  the  atmosphere.  Since  we  are  living  at  the 
bottom  of  an  ocean  of  air,  and  this  air  is  a  fluid  which  has  weight, 

it  is  natural  to  expect  that  it 
exerts  a  pressure.  Ordinarily  we 
are  not  aware  of  this  pressure, 
because  it  pushes  up  on  the  bot- 
toms of  objects  almost  as  much 
as  it  pushes  down  on  the  tops 

Fig.  104.     Removing  the  upward     of  them.      By  getting  rid  of  this 

pressure  <  upward  pressure  underneath,  we 

can  see  how  great  the  downward  pressure  on  top  really  is.    This 
can  be  done  with  a  vacuum  pump,  or  in  part  even  with  the  lungs. 

Let  us  fasten  a  piece  of  sheet  rubber  over  the  end  of  a  thistle  tube,  as 
shown  in  figure  104.  If  we  suck  the  air  out  of  the  bulb  with  the  mouth, 
the  rubber  is  forced  downward  by  the  atmospheric  pressure. 


TORRICELLPS  EXPERIMENT 


101 


Fig.    105.     Pressure  of  the  air 
breaking  a  membrane. 


This  experiment  is  even  more  striking  when"  performed  with  a  larger 
membrane  and  with  a  vacuum  pump.  If  we  tie  a  piece  of  rubber  over 
the  mouth  of  the  glass  vessel  shown  in 
figure  105,  and  gradually  pump  out  the 
air,  the  rubber  will  be  pushed  down  more 
and  more  by  the  pressure  of  the  air 
above  it,  until  it  finally  bursts.  If  a 
piece  of  bladder  is  used  instead  of  rub- 
ber, it  will  break  with  a  loud  report. 

One  of  the  most  interesting  of 
Otto  von  Guericke's  experiments 
was  that  with  his  famous  "  Magde- 
burg hemispheres."  These  were 
two  hollow  hemispheres  about  22 
inches  in  diameter  wjiich  fitted 
together  so  well  that  the  air  could 
be  pumped  out  from  between  them. 
The  pressure  of  the  surrounding 
atmosphere  then  held  them  together 
firmly.  In  a  test  before  the  Reichstag  and  the  Emperor,  it 
required  sixteen  horses,  four  pairs  on  each  hemisphere,  to  pull 
them  apart  (Fig.  106). 

88.  "  Nature  abhors  a  vacuum."     The  ancients   tried   to 
explain  many  phenomena  by  saying  that  "  nature  abhors  a 
vacuum";   but  when  the  great   Italian  philosopher,   Galileo 
(Fig.  107),  found  that  a  suction  pump  would  not  raise  water 
more  than  33  feet,  he  remarked  that  nature's  horror , of  a  vacuum 
was  a  curious  emotion  if  it  stopped  suddenly  at  33  feet.     He 
already  knew  both  that  air  has  weight  and  that  the  "  resistance 
to  a  vacuum  "  was  measured  by  a  column  of  water  about  33  feet 
high.     Yet  he  left  it  to  his  friend  and  successor,  Torricelli, 
to  unite  these  two  ideas. 

89.  Torricelli's  experiment.     In   1643,  Torricelli  devised  >a 
means  of  measuring  this  "  resistance  "  which  nature  "  offers 
to  a  vacuum  "  by  a  column  of  mercury  in  a  glass  tube  instead 
of  a  column  of  water. 


102 


MECHANICS  OF  GASES 


ATMOSPHERIC  PRESSURE 


103 


We  may  repeat  this  experi- 
ment if  we  take  a  stout  glass 
tube  about  3  feet  long,  closed 
at  one  end,  and  fill  it  com- 
pletely with  mercury.  If  we 
close  the  opening  with  the 
finger,  invert  the  tube,  and  put 
its  open  end  into  a  dish  of  mer- 
cury, we  observe  that,  when  the 
finger  is  removed,  the  mercury 
in  the  tube  (Fig.  108)  sinks  to 
a  level  about  30  inches  above 
the  mercury  surface  in  the  dish 
(if  this  experiment  is  done  at 
sea  level).  If  we  incline  the 
tube  to  one  side,  the  metal 
fills  the  entire  tube  and  hits 
the  top  of  the  glass  with  a 
sharp  click.  The  space  above  F- 
the  mercury  is  empty  except 
for  a  minute  quantity  of  mer- 
cury vapor.  It  is,  indeed,  the 

most   perfect   vacuum  that  we  know  how  to 

make. 

The  column  of  mercury  in  the  tube  just 
balances  the  pressure  of  the  atmosphere 
on  the  mercury  in  the  larger  vessel.  In 
other  words,  liquids  rise  in  exhausted 
tubes  because  the  pressure  exerted  by  the 
atmosphere  on  the  surface  of  the  liquid 
outside  pushes  the  liquid  up  the  tube,  and 
not  because  of  any  mysterious  sucking 
power  created  by  the  vacuum. 

90.  How  to  calculate  the  pressure  of  the 
atmosphere  from  Torricelli's  experiment. 

Fig.   108.     Torriceiii's  From  the  law  that  P^ssure  in  a  liquid  is 
experiment— baianc-  everywhere  the  same  at  the  same  depth, 

the  air6  w^th8  aUImer-  we  ^now  tnat  when  the  mercury  is  held 
cury  column.  up  in  the  inverted  tube,  the  pressure  in  the 


Galileo  Galilei  (1564-1642). 
Often  called  "  the  father  of  modern 
science  "  because  he  was  one  of  the  first 
to  test  his  theories  with  experiments. 


104  MECHANICS  OF  GASES 

tube  at  a  (Fig.  109)  is  the  same  as  at  the  surface  outside,  where 
it  is  exerted  by  the  atmosphere.  At  a  it  is  exerted  by  the 
column  of  mercury  ab.  Under  standard  conditions,  the  height 
ab  is  about  76  centimeters,  and  the  pressure  at  a  is  therefore 
equal  to  the  weight  of  a  column  of  mercury  76  centimeters 
high  and  1  square  centimeter  in  cross  section. 
vacuum  ^is  *s  ^ne  weight  of  76  cubic  centimeters  of 
mercury,  or  76  times  13.6  grams,  or  1034  grams. 
In  the  English  system  the  pressure  of  the 
atmosphere  is  equal  to  the  weight  of  a  column 
^  of  mercury  about  30  inches  high  and  1  square 
inch  in  cross  section ;  that  is,  30  X  0.49,  or 
14.7  pounds.  Roughly,  then,  one  "atmosphere  " 
is  about  1  kilogram  per  square  centimeter,  or  about 
|  15  pounds  per  square  inch. 

91.  Pascal's  experiments.     In  1648,  Pascal 
reasoned  that  if  the  mercury  column  were  held 
up  simply  by  the  pressure  of  the  air,  the  column 
Fig.  109.    Meas-  OUght  to  foe  shorter  at  a  high  altitude.     So  he 

urmg  the  pres- 

sure  of  the  air  carried  a  Torricelli  tube  to  the  top  of  a  high 

with  a  mercury    tower  in    parj      and    found    ft  gli  ht    fall   in   the 
column.  ,  .   . 

height  of  the  mercury  column.  Desiring  more 
decisive  results,  he  wrote  to  his  brother-in-law  to  try  the  experi- 
ment on  a  mountain  in  southern  France.  In  an  ascent  of  1000 
meters,  the  mercury  sank  about  8  centimeters,  which  greatly 
delighted  and  astonished  them  both. 

Pascal  also  tried  TorricellFs  experiment,  using  red  wine 
and  a  glass  tube  46  feet  long,  and  found  that  with  a  lighter 
liquid  a  higher  column  was  sustained  by  the  air  pressure. 

92.  The  barometer.  The  arrangement  constructed  by 
Torricelli  may  be  set  up  permanently  as  a  means  of  measur- 
ing the  pressure  of  the  atmosphere.  It  is  then  called  a  ba- 
rometer. To  "  read  the  barometer  "  means  simply  to  meas- 
ure accurately  the  height  of  the  mercury  column  above  the 
surface  of  the  liquid  in  the  reservoir.  In  the  form  of  barometer 


USES  OF   THE  BAROMETER 


105 


JSL 


shown  in  figure  110,  this  reservoir  has  a  flexible  bottom  which 
may  be  raised  so  as  to  bring  the  surface  of  the  pool  of  mercury 
just  up  to  the  tip  of  an  ivory  point  projecting  into  the  reservoir. 
The  height  of  the  mercury  in  the  tube  is  then 
read  off  on  a  scale  attached  to  the  tube. 

A  more  convenient  form  to  carry  about  is  the 
aneroid,  or  metallic  barometer  (Fig.  111).  As  the 
name  indicates,  it  is  "  without  liquid,"  and  consists 
essentially  of  a  disk-shaped  metal  box,  which  has 
a  thin  corrugated  top.  When  the  air  has  been 
pumped  out  of  the  box,  it  is  sealed  up,  its  top 
being  supported  by  a  stout  spring  to  prevent  its 
collapsing.  As  the  pressure  of  the  air  changes,  the 
top  of  the  box  moves  up  or  down,  and  the  small 
motion  is  greatly  magnified  by  means  of  levers  and 
a  delicate  chain,  and  is  communicated  to  a  pointer 
which  moves  over  a  scale.  A  hairspring  serves  to 
take  up  the  slack  of  the  chain.  The  scale  is  grad- 
uated to  correspond  to  the  readings  of  a  standard 
mercurial  barometer.  Aneroid  barometers  are  made 
in  various  sizes.  Some  are  even  as  small  as  ordinary 
watches. 

93.  Uses  of  the  barometer.  The  barometer 
indicates  changes  in  atmospheric  pressure. 
These  changes  may  be  due  to  fluctuations  in 
the  atmosphere  itself  or  to  changes  in  the  ele- 
vation of  the  observer. 

If  a  barometer,  kept  always  at  the  same 
elevation,  is  frequently  observed,  or  if  it 
makes  a  continuous  record,  as  does  a  barograph 
(Fig.  112),  it  is  found  to  fluctuate  accord- 
ing to  the  weather.  Experience  shows  that  a 
"  falling  barometer,"  that  is,  a  sudden  decrease 
of  atmospheric  pressure,  precedes  a  storm ;  and 


Fig.  no.  Mer- 
cury barometer. 
(Fortin  type.) 


a  "  rising  barometer,"  that  is;  an  increasing  atmospheric  pres- 
sure, indicates  the  approach  of  fair  weather;  while  a  steady 
"  high  barometer  "  means  settled  fair  weather. 


106 


MECHANICS  OF  GASES 


The  Weather  Bureau  takes  barometric  readings  simultaneously 
at  many  different  places,  and  the  results  are  telegraphed  to  central 
stations,  where  weather  maps  are  prepared.  On  these  maps  it  is 
observed  that  there  are  certain  broad  areas  where  the  pressure  is  low, 


Pointer 


nspnng 
Vacuum  box 


Fig.  in.     Aneroid  barometer  with  diagram  to  show  its  principle. 

and  other  regions  where  the  pressure  is  high.  The  areas  of  low  bar- 
ometric pressure  are  usually  storm  centers,  which  generally  move  in  an 
easterly  direction.  If  we  know  where  these  low-pressure  areas  are 
located  and  their  prob'able  movement,  we  may  predict  the  weather. 


^  Fig.  112.     Barograph,  or  self-recording  barometer. 

Figure  113  shows  a  portion  of  a  government  weather  map.  The  curved 
lines,  showing  the  places  where  the  barometric  pressure  is  equal,  are 
called  isobars.  The  direction  of  the  wind  at  various  places  is  indi- 
cated by  an  arrow.  A  careful  study  of  these  phenomena  (which 
is  called  meteorology)  shows  that  "  lows  "  are  really  great  eddies  of  air 
slowly  moving  in  a  counter-clockwise  direction. 


USES  OF   THE  BAROMETER 


107 


Another  important  use 
of  the  barometer  is  to 
measure  the  difference  in 
altitude  between  two 
places.  If  a  surveyor  or 
explorer  carries  a  barome- 
ter up  a  mountain,  he 
notices  that  it  indicates 
a  decrease  in  atmospheric 
pressure  as  he  ascends. 
For  places  not  far  above 
sea  level  this  decrease  is 
about  1  millimeter  for 
every  11  meters  of  eleva- 
tion, or  0.1  of  an  inch  for 
every  90  feet  of  ascent. 
Aneroid  barometers  grad- 
uated in  feet  or  meters 


Fig.  113.     Portion  of  a  weather  map. 


40,000 


30,000 


20.000 


are  carried  by  balloon- 
ists  and  aviators  to 
tell  how  high  they 
are.  The  curve  in 
figure  114  shows  the 
average  atmospheric 
pressure  at  various 
altitudes.  The  maxi- 
mum altitude  shown 
for  an  airplane  has 
probably  already  been 
exceeded.  It  will  be 
seen  that  the  rate  of 
decrease  in  pressure  is 
o  10  *o  30  not  uniform  but  be- 

Barometmc  pressures,  ^ncnes 

«.  ~          .  .  ..      .   .          comes  less  at  high  alti- 

Fig.  114.     Curve   showing   the   relation   between 

atmospheric  pressure  and  altitude.  tudes.      Why  ? 


10,000 


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108 


MECHANICS  OF  GASES 


QUESTIONS  AND  PROBLEMS 

1.  Why  is  it  not  necessary  to  hang  a  barometer  out  of  doors  to 
measure  atmospheric  pressure  ? 

2.  Why  is  it  necessary  to  hang  a  mercurial  barometer  in  a  vertical 
position  ? 

3.  In  repeating  Torricelli's  experiment,  why  is  it  necessary  to  have 
the  bore  of  the  tube  and  the  mercury  very  clean  ? 

4.  Why  does  a  rubber  tube  often  collapse  when  the  air  inside  is 
exhausted  ? 

5.  Otto  von  Guericke  is  said  to  have  built  a  water  barometer  which 
projected  above  the  roof  of  his  house.     A  wooden  image  floated  on  the 

surface  of  the  water  in  the  tube.     Why  are 
water  barometers  not  generally  used? 

6.  A  diver  works  51  feet  below  the  sur- 
face of  fresh  water.     To  how  many  atmos- 
pheres of  pressure  is  he  subjected  ? 

7.  When  the  barometer  reads  74.5  centi- 
meters, how  mt*iy  inches  does  it  read? 

8.  When  a  mercury  barometer  reads  76 
centimeters,  what  does  a  glycerin  barometer 
read?      (The  density  of  glycerin  is   1.26 
grams  per  cubic  centimeter.) 

9.  When  the  barometer  reads  75  centi- 
meters, what  is  the  atmospheric  pressure 
in  grams  per  square  centimeter? 

10.  During    a    storm    the     barometer 
Water    "dropped  "  1.5  inches.     How  far  would  a 

water  barometer  have  fallen  ? 

11.  If  a  certain  pressure  is  75  pounds 
per  square  inch,  how  many  kilograms  per 
square  centimeter  is  it  ? 

12.  During  a  mountain  climb  the  barometer  falls  1.75  inches.     What 
is  the  net  height  climbed  (in  feet)  ? 

13.  Two  glass  tubes  are  arranged  vertically  (Fig.  115)  so  that  their 
lower  ends  dip  into  water  and  kerosene,  respectively,  while  their  upper 
ends  are  joined  to  a  mouthpiece.     When  some  of  the  air  in  the  tubes  is 
sucked  out,  the  water  rises  26  centimeters  and  the  kerosene  33  centi- 
meters.    Find  the  specific  gravity  of  the  kerosene.     (This  is  a  common 
way  of  getting  specific  gravity.) 


Kerosene 


Fig.  115.     Specific  gravity  by 
balanced  columns. 


PUMPS   FOR  LIQUIDS 


109 


14.  The  original  Magdeburg  hemispheres  are  preserved  in  a  museum 
in  Munich.  They  are  about  22  inches  in  diameter  inside.  When  the 
air  was  exhausted,  it  is  said  to  have  required  8  horses  on  each  half  to 
separate  them.  Assuming  that  the  pressure  of  the  atmosphere  was 
15  pounds  per  square  inch,  find  the  force  exerted  by  each  set  of  horses. 
(Hint.  —  Reckon -force  on  circle  22  inches  in  diameter.  Why?) 

16.  In  the  apparatus  of  figure  115,  if,  after  the  columns  are  sucked 
up  and  the  pinch-cock  on  the  rubber  mouthpiece  is  screwed  up  tight, 
a  tiny  hole  were  bored  through  the  wall  of  the  glass  tube  halfway  up  the 
water  column,  would  the  water  in  the  upper  part  of  the  tube  run  out 
through  the  hole? 

PRACTICAL  EXERCISE 

Making  a  barometer.  Construct  a  J-tube  mercurial  barometer. 
Use  strong  glass  tubing  (about  1  cm.  diameter).  It  is  easier  to  fill  the 
tube  if  the  bend  is  made  of  thick-walled  rubber 
tubing.  Mount  it  on  a  board  and  use  a  sliding 
meter  stick  to  measure  the  height  of  the  mercury 
column. 

94.  Pumps  for  liquids.  The  ancients  used 
pumps  to  lift  water  from  wells,  even  though 
they  did  not  know  why  a  pump  works ;  they 
thought  it  was  because  "  nature  abhors  a 
vacuum."  We  know  now  that  the  under- 
lying principle  is  the  same  as  in  a  mercurial 
barometer :  it  is  the  pressure  of  the  atmos- 
phere on  the  surface  of  the  water  in  the  well 
that  pushes  the  water  up  into  the  pump. 

The  ordinary  suction  pump  (Fig.  116)  consists 
of  a  cylinder  C,   which  is  connected  with   the 
well  or  cistern  by  a  pipe  T.     At  the  bottom  of  Fi8-  "?•    A  suction  or 
the  cylinder  is  a  clapper  valve  S,  opening  up.     A  pump, 

piston  P  can  be  worked  up  and  down  in  the  cylinder  by  means  of  a 
handle.  This  piston  also  contains  a  valve  V  opening  up.  On  the  up- 
stroke of  the  piston  P,  the  valve  V  remains  closed  because  of  its  weight 
and  the  pressure  of  the  water  and  air  above  it.  Between  the  piston 
and  the  bottom  of  the  cylinder  there  would  be  a  partial  vacuum,  if  the 
valve  S  remained  closed.  But  the  pressure  of  the  air  on  the  water  in 
the  well  forces  some  water  up  through  the  pipe  T,  past  the  valve  S  into 


110 


MECHANICS  OF  GASES 


the  cylinder  C.  On  the  down  stroke  of 
the  piston  the  valve  S  closes,  the  valve  V 
opens,  and  the  water  gets  above  the 
piston.  On  the  next  up  stroke  it  is 
lifted  out  through  the  spout.  The  valve 
S  must  never  be  more  than  34  feet  above 
the  water  in  the  well,  and  in  practice 
this  distance  is  seldom  more  than  30 
feet.  Why? 

Another  kind  of  pump,  shown  in 
figure  117,  is  called  a  force  pump.  The 
suction  pipe  T  with  its  valve  S  are 
exactly  like  the  corresponding  parts  of 
the  house  pump  just  described,  but  the 
piston  has  no  opening  through  it,  and 
the  outlet  pipe  and  a  second  valve  are 
at  the  bottom  of  the  cylinder.  Raising 
the  piston  fills  the  cylinder  with  water  ; 
pushing  it  down  again  forces  the  water 
out  through  the  second  pipe.  If  enough 
force  is  exerted  on  the  piston,  the  water 
can  be  pushed  up  to  a  considerable 

height.     The  pump  can  therefore  be  located  near  the  bottom  of  a  well 

or  mine  shaft. 

Since  the  water  is  forced  up  only  on 

the  down  stroke,  it  comes  in  spurts.      To 

reduce  the  jar  and  shock,  an  air  chamber  A 

is  connected  with  the  delivery  pipe,  so  that 

the  air  may  act  as  a  cushion  or  spring. 

Power  pumps,   such  as  are  used  on   fire 

engines  or  in  city  waterworks,  are  "  double- 
acting  "  (Fig.  118),  and  give  a  still  steadier 

stream. 

When  a  large  volume  of  water  is  to  be 

lifted  a  short  distance,  a  centrifugal  pump 

(Fig.  119)  is  used.     This  is  something  like 

a  water  wheel  worked  backwards.     As  the 

wheel  inside  (Fig.  120)  is  turned,  the  water, 

which   enters  near  the  hub,  gets  caught 

between  the  blades  and  is  hurled  outward 

into  the  delivery  space  around  the  wheel, 

even  against  some  pressure  there.     Cen- 


117.     A  force  pump  with 
an  air  dome. 


ivery 


Fig.  118.  A  double-acting 
force  pump  with  air  cushion 
on  top. 


SIPHON 


111 


trifugal  pumps  are  often  used  to  circulate  the  water  in  the  cooling 
system  of  automobiles  and  also  to  circulate  the  oil.  Similar  machines, 
called  blowers,  are  used  to  force  a  current  of  air  through  a  building 
for  ventilation,  to  make  "  forced  draft  "for  furnaces,  and  to  create 


Fig.  119.     Centrifugal  pump.      The  water 
is  drawn  in  near  the  center  on  both  sides. 


Fig.  1 20.     Vertical  section  of 
a  centrifugal  pump. 


the  suction  in  portable  vacuum  cleaners.  Often  several  of  these  blowers 
are  used  in  series  to  give  higher  pressures.  Large  blowers,  driven  by 
steam  turbines,  are  used  with  blast  furnaces,  because  of  the  extremely 
steady  rate  at  which  they  furnish  the  air  needed  for  combustion. 

95.  Siphon.  The  siphon  is  a  bent  tube  with 
.unequal  arms.  It  is  used  to  empty  bottles 
and  tanks  which  cannot  be  easily  tipped,  or  A 
to  draw  off  the  liquid  from  a  vessel  without 
disturbing  the  sediment  at  the  bottom.  If 
the  tube  is  filled  and  placed  in  the  position 
shown  in  figure  121,  the  liquid  will  flow  out 
of  the  vessel  A  and  be  discharged  at  a  lower 
level  D.  The  force  which  makes  it  flow  is  the 
weight  of  the  column  of  water  CD,  which  is 
between  the  water  level  A  A'  and  the  water 
level  DD'.  If  the  water  level  DD'  is  raised 
to  A  A',  "this  moving  force  becomes  nothing  Fie-121-  Asiphon. 
and  the  water  ceases  to  flow ;  if  the  level  DD'  is  lifted  above 
A  A',  the  liquid  flows  back  into  the  vessel  A.  A  siphon  works, 
then,  as  long  as  the  free  surface  of  the  liquid  in  one  vessel 


112  MECHANICS  OF  GASES 

is  lower  than  the  free  surface  of  the  liquid  in  the  other  vessel. 
A  water  siphon  will  not  work  if  the  top  of  the  bend  B  is  more 
than  34  feet  above  the  level  A  A'.  Why? 

Siphons  are  often  used  on  a  large  scale  in  engineering.  For  instance, 
in  power  plants  the  water  used  to  condense  the  steam  is  often  taken 
from  the  ocean,  raised  10  or  15  feet  to  the  condenser,  and  carried  back 
to  the  ocean,  through  a  pipe  that  is  everywhere  air-tight  and  acts  like  a 
siphon.  The  only  work  that  the  pumps  have  to  do  is  to  keep  the  water 
moving  against  the  friction  in  the  pipe.  Siphons  are  also  used  in  aque- 
ducts to  carry  water  over  hills.  In  such  cases  air  bubbles  carried  along 

in  the  water  tend  to  collect  at  the  top  of 
each  hill,  and  so  small  air  pumps  have 
to  be  installed  to  keep  the  pipes  full  of 
water. 

Siphon  action  also  plays  a  part  in 
modern  water-closets  (Fig.  122).  The 
siphon  EAD  is  not  completely  filled  with 
water,  but  the  shape  of  the  long  arm  AD 
is  such  that  the  sheet  of  water  that  flows 
over  the  lip  at  A  strikes  successively  at 
B,  C,  and  D.  making  gas-tight  seals  across 
the  pipe.  Meanwhile,  the  flowing  water 
carries  air  along  with  it,  producing  a 
partial  vacuum  near  A.  This  sucks  over  the  water  in  the  bowl  until 
the  level  drops  far  enough  to  let  air  flow  past  the  seal  at  E.  In  jet- 
siphon  closets  an  auxiliary  jet  J  (Fig.  122)  is  fed  from  the  water 
supply  F  by  a  diagonal  passage  along  the  side  of  the  bowl.  This  jet 
points  up  the  short  leg  EA  and  helps  to  get  the  flow  started  quickly  and 
quietly. 

PRACTICAL  EXERCISE 

Rate  of  flow  of  a  siphon.  Measure  the  time  required  to  empty  a 
given  pail  of  water  with  a  siphon.  Repeat,  using  a  longer  tube  and 
greater  difference  in  level.  Study  the  effect  of  increasing  the  height 
from  the  water  in  the  pail  to  the  bend  in  the  siphon. 

96.  The  buoyancy  of  air.  We  have  seen  that  as  one  climbs 
a  mountain,  the  pressure  of  the  air  decreases.  A  sensitive 
barometer  will  indicate  a  decrease  of  pressure  even  when  it 
is  lifted  from  the  floor  to  a  table.  Therefore  the  upward 
pressure  of  the  air  on  the  bottom  of  any  object  is  slightly 


BALLOONS  AND  AIRSHIPS 


113 


more  than  the  downward  pressure  of  the  air  on  its  top.  In 
other  words,  just  as  in  the  case  of  liquids,  there  is  a  lifting 
effect  on  everything  surrounded  by  air. 
This  lifting  effect  is  equal  to  the  weight 
of  the  air  which  is  displaced  (Principle 
of  Archimedes). 


To  make  this  principle  of  the  buoyancy 
of  the  air  seem  more  real,  let  us  balance  a 
hollow  brass  globe  against  a  solid  piece  of 
brass  under  the  receiver  of  a  vacuum 
pump  (Fig.  123).  When  the  air  is  pumped 
out,  the  globe  seems  to  be  heavier  than 
the  solid  brass  weight,  because  the  sup- 
port of  the  air  around  it  has  been  with- 
drawn. If  the  air  is  readmitted  rapidly,  Fie- 
the  rise  of  the  globe  will  be  very  apparent. 


Lifting  effect  of  air. 


Most  things  are  so  heavy  in 
comparison  with  the  amount  of  air 
they  displace  that  this  loss  in 
weight,  due  to  the  buoyancy  of  the 
air,  is  not  taken  into  account.  For 
example,  a  barrel  of  flour  would 
weigh  about  8  ounces  more  in  vacua 
than  in  air.  But  if  the  volume  of 
air  displaced  is  very  large  in  com- 
parison with  the  weight,  as  in  the 
case  of  a  balloon,  the  object  is 
lifted  just  as  a  piece  of  wood  is 
lifted  when  immersed  in  water. 

97.  Balloons  and  airships.  The 
envelope,  or  bag,  of  a  balloon  (Fig. 
124)  is  made  of  two  or  three  layers 
of  thin  rubberized  cotton  or  silk 
cloth,  or  sometimes  of  goldbeater's  skin  strengthened  with 
cloth,  so  as  to  be  light,  strong,  and  as  nearly  gas-tight  as  possible. 


Fig.   124. 


U.  S.  Army  spherical 
balloon. 


114 


MECHANICS  OF  GASES 


Free  balloons  are  spherical  because  this  gives  the  greatest 
volume  for  a  given  amount  of  fabric.  A  wicker  basket  to 
carry  passengers,  instruments,  and  ballast  is  suspended  from 
a  rigging,  which,  in  the  case  of  a  free  balloon,  is  a  great  net  of 
light  cords  that  envelops  the  balloon.  The  bag  is  usually  filled 
with  hydrogen,  although  illuminating  gas  or  even  heated  air 
may  be  used  for  short  trips. 

An  airship  is  a  dirigible  balloon  provided  with  propellers 
and  gasoline  engines  and  with  horizontal  and  vertical  rud- 
ders. An  airship  is  shaped  more  or  less  like  a  sausage  and 
has  a  pointed  nose  and  tail  so  as  to  reduce  the  head  resist- 
ance as  it  moves  through  the  air.  An  airship  of  the  Zeppelin 
type,  such  as  the  R-34  which  flew  across  the  Atlantic  in  1919, 


Tube  to  platform 
Gun 


Ventilating  shaft 


power  car  £  Ga^line  tanks  I  Power  ' 

Corridor  running  length  of  airship 

Fig.  125.     Dirigible  airship  of  the  rigid  type. 


"Length  644  ft. 
Beam  79  ft. 
Height  91  ft. 


has  a  huge  rigid  framework  (Fig.  125),  made  of  a  very  light 
and  strong  alloy  of  aluminum,  and  covered  with  light,  weather- 
proof fabric.  Inside  are  15  to  20  separate  hydrogen  bags, 
each  in  a  compartment  of  the  frame.  The  crew  of  such  an 
airship  can  climb  all  over  its  interior  between  the  hydrogen 
bag  and  the  outer  envelope  to  make  repairs.  In  the  smaller 
types  there  is  only  one  gas  bag,  which  is  held  in  shape  by  the 
excess  pressure  of  the  gas  inside.  In  nonrigid  ships  (Fig.  126), 
one  or  more  cars  are  suspended  by  cables  attached  to  reenforcing 
patches  sewed  to  the  fabric  of  the  bag.  In  semirigid  ships, 
there  is  a  stiff  keel  the  whole  length  of  the  bag,  which  gives 
it  some  stiffness  and  carries  the  cars. 

One  great  danger  in  ballooning  is  from  fire.     In  war  time 


HELIUM   AIRSHIP 


115 


•s 


116  MECHANICS  OF  GASES 

incendiary  bullets  are  used,  and  in  times  of  peace  the  balloon 
fabric  sometimes  gets  electrified  by  friction  and  a  spark  dis- 
charge may  ignite  the  hydrogen.  Also  the  hot  exhaust  from 
the  engine  is  a  constant  source  of  danger.  Recently  helium 
(see  figure  126),  a  non-inflammable  gas,  has  been  separated 
from  certain  special  kinds  of  natural  gas  in  such  quantities  that 
it  will  probably  be  used  in  the  airships  of  the  future  as  a 
measure  of  safety  against  fire. 

To  compute  the  total  lift  of  a  balloon,  we  have  only  to  get 
the  difference  between  the  weight  of  the  air  displaced  and  the 
weight  of  the  gas  in  the  balloon.  A  large  part  of  the  total  lift 
is  used  in  raising  the  weight  of  the  bag,  rigging,  and  car  and, 
in  a  dirigible,  of  the  engines.  The  rest,  the  disposable  lift, 
is  available  for  lifting  ballast,  fuel,  passengers,  and  freight. 

QUESTIONS  AND  PROBLEMS 

1.  How  many  feet  could  water  be  lifted  with  a  perfect  suction  pump 
(a)  at  sea  level,  and  (6)  in  Denver,  Colorado  (altitude  about  5400  ft.)  ? 

2.  How  many  feet  could  crude  oil  (density  0.89  grams  per  cubic 
centimeter)  be  lifted  out  of  an  oil  well  by  a  perfect  suction  pump  at  sea 
level? 

3.  How  much  work  is  needed  to  lift  100  gallons  of  water  25  feet  with 
a  perfect  pump  ? 

4.  How  much  power  is  needed  to  raise  100  gallons  of  water  per 
minute  25  feet  with  a  perfect  pump? 

6.  A  force  pump  is  to  deliver  water  at  a  point  20  feet  above  the  level 
of  its  barrel.  How  great  is  the  water  pressure  in  the  barrel  when  the 
piston  is  descending? 

6.  The  piston  of  a  fire-engine  force  pump  is  4  inches  in  diameter,  and 
the  total  force  exerted  on  it  by  the  engine  is  600  pounds.     If  the  pump 
acts  perfectly,  at  how  great  a  height  will  it  deliver  water? 

7.  A  siphon  is  to  be  used  to  transfer  mercury  from  one  bottle  to 
another.     How  far  above  the  level  of  the  mercury  in  the  higher  bottle 
can  the  top  of  the  siphon  tube  be  ? 

8.  What  is  meant  by  "priming"  a  dry  suction  pump?     Explain 
how  this  process  restores  the  pump  to  working  condition. 


AIR  COMPRESSORS 


117 


9.   Explain  the  operation  of  the  S-trap  used  under  sinks  and  wash- 
bowls (Fig.  127).     Why  should  such  traps  be  ventilated? 

10.  How  would  one  clean  and  empty  an 
S-trap? 

11.  A  balloon  has  a  capacity  of  37,000 
cubic  feet  and  is  filled  with  95  per  cent  pure 
hydrogen  (the  rest  being  air).     The  balloon, 
rigging,  and  basket  weigh  1000  pounds,  and 
the  two  passengers  each  150  pounds.     How 
much  pull  is  required  to  hold  the  balloon  down 
near  the  ground?     (Assume  the  density  of 
hydrogen  is  0.0053  pounds  per  cubic  foot.) 

12.  An  airship  has  a  capacity  of  84,000 
cubic  feet  and  is  filled  with  97  per  cent  hydro- 
gen.    The  weight  of  the  gas  bag  and  asso- 
ciated parts  is  2070  pounds,  the  weight  of  the  „ 

j*     i  mon  j  Fig.  127.     A  washbowl  and 

engine,  car,  tanks,  and  fuel  1930  pounds,  and  S-trap. 

the  weight  of  the  instruments,  parachutes, 

tools,  etc.  is  350  pounds.  If  it  carries  two  men  weighing  together  320 
pounds,  how  many  pounds  of  ballast  are  needed  to  give  exact  equili- 
brium ? 

13.  The  total  lift  of  the  R-34  when  filled  with  hydrogen  is  about 
70  tons.     Helium  is  twice  as  dense  as  hydrogen.    What  would  be  the. 
total  lift  of  the  R-34  if  filled  with  helium? 

AIR  UNDER  PRESSURE 

98.  Pascal's  law  applies  to  gases.     Gases  under  pressure  act 
exactly  like  liquids  under  pressure  in  that  each  transmits  pres- 
sure undiminished  in  all  directions,  and  on  all  parts  of  the  in- 
closing wall. 

99.  Air  compressors.     The  vacuum  pump  described  in  section 
85  could  also  be  used  as  an  air  compressor  to  pump  air  from 
the  atmosphere  into  a  closed  tank  by  attaching  a  tube  at  B. 
The  pressure  that  could  be  obtained  in  the  tank  would  depend 
on  the  force  applied  to  the  pump  handle.     Automobile  tires 
require  a  pressure  of  from  45  to  75  pounds  per  square  inch ;  for 
this  purpose  a  pump  driven  by  an  electric  motor  or  a  two- 
cylinder  hand  pump  is  generally  employed. 


118 


MECHANICS  OF  GASES 


The  hand  pump  shown  in  figure  128  consists  of  two  cylinders  C  and  c 
and  two  pistons  attached  to  a  common  handle.  The  loosely  fitting 
metal  pistons  are  provided  with  two  cup-shaped  leather  washers :  the 
one  on  the  large  piston  P  is  turned  down,  and  the 
one  on  the  smaller  piston  p  is  turned  up.  On  the 
down  stroke  of  the  pistons,  the  air  below  P  is 
forced  over  through  the  connecting  passage  at  the 
bottom  into  the  small  cylinder,  and  then  up  past 
its  piston  into  the  hose  and  tire.  On  the  up 
stroke,  the  compressed  air  above  p  is  forced  into 
the  tire ;  and  at  the  same  time  air  from  the  outside 
passes  P  and  fills  both  cylinders.  The  valve  in  the 
stem  of  the  tire  and  the  valve  V  in  the  pump  keep 
the  air  from  flowing  back  into  the  small  cylinder  c. 
Thus  we  see  that  a  two-cylinder  pump  is  more  effec- 
tive than  a  one-cylinder  pump,  because  it  forces  air 
into  the  tire  on  both  the  up  and  the  down  strokes. 

Large   air   compressors   driven   by   steam 
p.     I2g    Two_c  jjn_  engines  or  electric  motors  are  much  used  in 
der  automobile-tire  steel  plants,  shops,  and  quarries  to  furnish 
a  supply  of  compressed  air.     This  is  delivered 
as  a  forced  draft  to  blast  furnaces,  or  stored  in  steel  tanks  and 
used  to  drive  all  sorts  of  pneumatic  machinery. 

100.  Uses  of  compressed  air.     There  are  many  tools  which 
are  driven  by  compressed  air,  such  as  riveting  hammers  for 
forming   the   rivet-heads   on   steel  work,  and  the   pneumatic 
tools  used  in  stone  cutting,  iron  chipping,  drilling,  etc.     These 
are,  in  general,  lighter  and  simpler  than  other  portable  tools, 
and  there  is  less  danger  of  fire.     When  such  tools  are  used 
in  mines,  the  waste  air  which  they  discharge  helps  to  furnish 
ventilation,  and  this  is  often  an  important  advantage.     Rock 
drills,  sand  blasts  for  cleaning  metal  and  stone  surfaces,  and 
air  brakes  on  electric  and  steam  cars  are  other  common  applica- 
tions.    Compressed  air  is  also  used  to  keep  the  water  out 
of  diving  bells  and  the  open  ends  of  tunnels  while  they  are 
being  built  under  rivers  or  harbors,  and  to  supply  air  to  divers. 

101.  Air  is  very  compressible.     A  striking  difference  between 
compressed  air  and  water  under  pressure  is  that  the  volume 


BOYLE'S  LAW  119 


of  the  air  is  much  reduced  by  the  pressure  while 
the  water  is  compressed  almost  not  at  all.  This 
striking  difference  can  be  shown  by  the  follow- 
ing experiment. 


When  a  brass  tube,  with  a  closely  fitting  steel  rod 
(Fig.  129),  is  filled  with  air,  the  plunger  can  easily  be 
pushed  down  by  hand.     When  the  plunger  is  released, 
it  springs  back  nearly  to  its  initial  position.     If  it  does 
not  quite  come  back  to  its  initial  position,  it  means  that 
some  of  the  air  has  leaked  out.    The  entrapped  air  acts 
like  a  spring.     But  when  the  tube  is  filled  with  water, 
or  any  other  liquid,  it  is  quite  impossible  to  push  the  Fig.  129.   Corn- 
plunger  down  to  any  perceptible  extent  by  hand ;  and      possibility  of 
when  the  end  of  the  plunger  is  struck  with  a  hammer,      fluids- 
the  effect  is  as  if  the  entire  tube  were  a  solid  steel  column,  because 
the  liquid  is  so  nearly  incompressible. 

This  ability  of  air  to  yield  to  a  shock  and  to  return  promptly 
to  its  original  condition  afterward,  that  is,  its  compressibility 
and  its  perfect  elasticity,  together  constitute  what  is  called  its 
resiliency.  This  characteristic  is  utilized  in  pneumatic  tires 
and  air  cushions  and  in  tennis  balls  and  footballs. 

102.  How  volume  of  air  changes  with  pressure  —  Boyle's 
law.  The  amount  of  change  in  the  volume  of  a  given  quantity 
of  air  when  the  pressure  changes  was  first  investigated  in  1662 
by  an  Irishman,  Robert  Boyle,  and  a  few  years  later  by  a  French- 
man, Mariotte. 

These  experiments  have  shown  that,  at  constant  temperature, 
the  volume  of  a  gas  varies  inversely  as  the  pressure.  This  prin- 
ciple is  known  as  Boyle's  law ;  it  applies  to  all  gases. 

This  may  also  be  expressed  in  symbols  as  follows: 

V       P1 

— ,  =  —      (notice  the  inverse  proportion), 

or  PV=P'V 

where  V  is  a  given  volume  of  gas  subjected  to  a  certain  pressure  P, 
and  V  the  changed  volume  when  the  pressure  changes  to  P'  at  constant 
temperature. 


120 


MECHANICS  OF  GASES 


We  may  investigate  this  question  for 
ourselves  by  performing  the  following  ex- 
periment. Figure  130  shows  a  large  iron 
cylinder  and  a  small  glass  tube  closed  at 
the  upper  end  and  connected  with  the  large 
cylinder  at  the  bottom.  A  pressure  gauge 
(Bourdon  type)  is  connected  to  indicate 
the  pressure  directly  in  pounds  per  square 
inch.  The  whole  apparatus  is  filled  about 
half  full  of  oil,  which  imprisons  a  certain 
amount  of  air  in  the  top  of  the  glass  tube. 
The  pressure  is  applied  by  means  of  a  com- 
pression pump  attached  at  the  top  of  the 
iron  cylinder.  Since  the  tube  is  uniform 
in  bore,  we  may  measure  the  volume  of 
the  air  within  in  terms  of  the  length  of  the 
air  column.  If  we  start  with  24  centi- 
meters of  air  in  the  tube  and  with  a  pres- 
sure of  15  pounds  per  square  inch,  and 
pump  in  air  until  the  pressure  is  doubled 
(30  Ibs./sq.  in.),  we  find  that  the  volume 
of  the  air  is  reduced  to  one  half  the  orig- 
inal volume  (that  is,  to  12  cm.).  If  we 
Fig.  130.  Apparatus  to  demon-  pump  in  more  air  until  the  pressure  is 
strate  Boyle's  Law.  tripled  (45  Ibs./sq.  in.),  we  find  that  the 

volume  of  the  air  is  reduced  to  one  third  (that  is,  to  8  cm.). 

Evidently,  if  the  pressure  on  a  certain  quantity  of  air  is 
doubled  and  the  volume  is  halved,  the  air  must  become  twice 
as  dense.  In  general,  the  density  of  air,  or  of  any  gas,  varies 
directly  as  the  pressure  at  constant  temperature. 

The  very  great  decrease  in  volume  that  can  be  produced 
by  a  sufficiently  high  pressure  is  made  use  of  in  storing  gases 
in  a  very  compact  form  for  transportation.  Thus,  oxygen 
gas,  which  is  used  for  welding  and  cutting,  for  the  treatment 
of  the  sick,  and  for  enabling  aviators  to  breathe  at  very  high 
altitudes,  is  sold  in  strong  steel  cylinders  into  which  it  has 
been  compressed  to  1800  pounds  per  square  inch. 

103.  Pressure  gauges.  Besides  barometers,  which  are 
really  pressure  gauges  designed  for  pressures  of  one  atmos- 


PRESSURE  GAUGES 


121 


phere  or  less,  we  need  gauges  for  higher  pressures,  such  as  those 
in  a  steam  boiler  or  a  compressed-air  tank,  and  gauges  for 
very  low  pressures,  such  as  those  in  the  con- 
denser of  a  steam  engine  or  the  receiver  of  a 
vacuum  pump. 

To  measure  slight  differences  in  pressure, 
the  open  manometer  is  employed,  usually  with 
some  liquid  lighter  than  mercury  as  the  indicat- 
ing fluid. 

If  we  bend  a  piece  of  glass  tubing  as  shown  in 
figure  131,  and  partly  fill  the  tube  with  colored 
water,  we  have  a  suitable  gauge  with  which  to 
measure  the  pressure  of  ordinary  illuminating  gas. 
This  will  usually  cause  a  difference  in  the  levels  A 
and  B  of  about  2  inches. 

For  high  pressures  this  form  of  gauge,  even 
when  filled  with  mercury,  becomes  too  cum- 
bersome, so  a  closed  manometer  (Fig.  132) 
is  used.  The  mercury  stands  at  the  same 
level  in  both  arms  when  the  pressure  is  one  atmosphere.  If  the 
pressure  is  greater  than  this,  the  mercury  is  forced  into  the 
closed  arm,  compressing  the  confined  air 
according  to  Boyle's  law.  The  scale  may 
be  made  to  read  in  atmospheres. 

For  practical  work  the  Bourdon  spring 
gauge  (section  76)  is  used.  Such  gauges 
are  usually  graduated  so  as  to  read  zero 
when  the  pressure  is  really  one  atmos- 
phere ;  that  is,  they  indicate  the  difference 
between  the  given  pressure  and  atmos- 
pheric pressure.  Therefore,  when  an  en- 
gineer speaks  of  a  pressure  of  100  pounds 
by  the  gauge,  he  means  100  pounds  per 
square  inch  above  one  atmosphere;  when  he  means  the  total 
pressure  above  a  vacuum,  he  usually  says  100  pounds  absolute. 


Fig.    131.      Open 
manometer. 


A— 


Fig.   132.     Closed  ma- 
nometer. 


122 


MECHANICS  OF  GASES 


When  pressures  less  than  one  atmosphere  are  to  be  measured,  such 
as  the  vacuum  in  the  condenser  of  a  steam  engine  (section  227),  a  ba- 
rometer of  the  ordinary  form  would  be  inconvenient,  because  the  whole 
reservoir,  or  cup,  at  the  bottom  would  have  to  be  exposed  to  the  pressure 
which  is  to  be  measured.  The  gauge  is,  therefore,  arranged  so  as  to 
admit  the  low  pressure  to  be  measured  to  the  top  of  the  barometer  tube. 
The  height  of  the  mercury  then  indicates  the  difference  between  the 
small  pressure  and  that  of  the  atmosphere.  The  better  the  vacuum, 
the  higher  such  a  gauge  reads.  Thus  engineers  usually  speak  of  a  26-  or 
a  28-inch  vacuum,  meaning  a  pressure  less  than  the  standard  30-inch 
atmosphere,  by  26  or  28  inches  of  mercury.  The  best  vacuums  now 
obtained  in  steam  turbine  condensers  are  from  29  to  29.5  inches. 
Since  these  mercury  gauges  would  be  inconvenient  in  engine  houses, 
Bourdon  gauges  are  used.  They  are  graduated  to  read  in  inches  like 
the  mercury  gauges  which  they  replace. 

PRACTICAL  EXERCISES 

1.  Blood  pressure.     Find  out  how   a   physician 
measures  a  patient's  blood  pressure.     Draw  a  careful 
diagram  of  the  apparatus.     What  is  the  function  of 
the  pressure  sleeve?     In  what  unit  is  blood  pressure 
expressed  ? 

2.  Gasoline  measuring  pump.    Figure  132A  shows 
a  common  type  of  gasoline  measuring  pump.     Is  it  a 
lift  or  a  force  pump?     Describe  carefully  its  construc- 
tion and  operation. 

QUESTIONS  AND  PROBLEMS 

(Assume  constant  temperature  in  these  problems.) 

1.  One  hundred  cubic  feet  of  air  under  a  pressure 
of  15  pounds  per  square  inch  absolute  are  compressed 
to  300  pounds  per  square  inch  absolute.     What  does 
the  volume  become  ? 

2.  The  volume  of  a  tank  is  2  cubic  feet,  and  it  is 
filled  with  compressed  air  until  the  pressure  is  3000 
pounds  per  square  inch  absolute.    How  many  cubic 
feet  of  air  under  a  normal  pressure  of  15  pounds  per 
square  inch  absolute  were  forced  into  the  tank  ? 

3.  An  oxygen  cylinder  charged  to  1800  pounds  per 
square  inch  absolute  contains  gas  enough  to  occupy 
200  cubic  feet  at  atmospheric  pressure.     What  is  the  Fig. 
internal  volume  of  the  cylinder  ? 


i32A.    Gaso- 
e  pump. 


ABSORPTION  OF  GASES  IN  LIQUIDS  123 

4.  What  is  the  net  force  applied  to  a  brake  piston  10  inches  in 
diameter,  when  the  pressure  by  the  gauge  is  80  pounds  per  square  inch  ? 
(Rememb'er  that  the  atmosphere  is  pressing  against  the  other  side  of 
the  piston.) 

5.  One  hundred  cubic  feet  of  air  at  a  pressure  of  15  pounds  per  square 
inch  are  compressed  to  36  cubic  feet.     What  is  the  pressure  then  ? 

6.  Oxygen  is  sold  in  steel  cylinders  under  a  pressure  of  1800  pounds 
per  square  inch  absolute.     As  the  gas  is  used,  the  pressure  drops. 
When  it  has  dropped  to  600  pounds  absolute,  what  fractional  part  of 
the  original  gas  remains  ?     Give  your  reasoning. 

OTHER  LESS  IMPORTANT  PROPERTIES  OF  GASES 

104.  Absorption  of  gases  in  liquids.  If  we  slowly  heat  a  beaker 
containing  cold  water,  small  air  bubbles  are  seen  to  collect  in  great  num- 
bers upon  the  walls  (Fig.  133)  and  to  rise  through  the 
liquid  to  the  surface.  It  might  seem  at  first  that 
these  are  bubbles  of  steam,  but  they  must  be  bubbles 
of  air,  first  because  they  are  formed  at  a  temperature 
below  the  boiling  point  of  water,  and  second  because 
they  do  not  condense  as  they  come  to  the  cooler  layers 
of  water  above. 

This  simple  experiment  shows  that  ordinary 
water  contains  dissolved  air,  and  that  the  amount 
of  air  which  water  can  hold  decreases  as  the 
temperature  rises.  It  is  the  oxygen  of  the  air  that  Fig.  133.  Bub- 
is  dissolved  in  water  which  supports  the  life  of  ^tser°f  **  in 
fish.  The  amount  of  gas  absorbed  by  a  liquid 
depends  on  the  pressure  of  the  gas  above  the  liquid.  Thus,  soda 
water  is  ordinary  water  which  has  been  made  to  absorb  large 
quantities  of  carbon  dioxide  gas  by  pressure.  When  the  pressure 
is  relieved,  the  gas  escapes  in  bubbles,  causing  effervescence. 
Careful  experiments  show  that  the  amount  of  gas  absorbed 
is  proportional  to  the  pressure.  The  amount  of  gas  which 
will  be  absorbed  by  water  varies  greatly  with  the  nature 
of  the  gas.  For  example,  at  0°C.  and  at  a  gas  pressure  of 
76  centimeters  of  mercury,  1  cubic  centimeter  of  water  will 


124  MECHANICS   OF  GASES 

absorb  0.049  cubic  centimeters  of  oxygen,  1.71  cubic  centi- 
meters of  carbon  dioxide,  and  1300  cubic  centimeters  of  ammonia 
gas.  The  ordinary  commercial  aqua  ammonia  is  simply 
ammonia  gas  dissolved  in  water. 

105.  Absorption  of  gases  in  solids.     Certain  porous  solids, 
such  as  charcoal,  meerschaum,  silk,  etc.,  have  a  great  capacity 
for  absorbing  gases.     For  example,   charcoal  will  absorb  90 
times  its  volume  of  ammonia  gas  and  35  volumes  of  carbon 
dioxide.     It  is  this  property  of  charcoal  which  makes  it  use- 
ful as  a  deodorizer.     This  absorption  seems  to  be  due  to  the 
condensation  of  a  layer  of  gas  on  the  surface  of  the  body  or 
of  the  pores  within  the  body.     Platinum  in  a  spongy  state 
absorbs  hydrogen  gas  so  powerfully  that  if  a  small  piece  is 
placed  in  an  escaping  jet  of  hydrogen,  the  heat  developed 
by  the  condensation  is  enough  to  ignite  the  jet.     This  has 
been  made  use  of  in  self-lighting  Welsbach  mantles. 

A  familiar  example  of  the  absorption  of  gases  by  liquid,} 
and  solids  is  the  contamination  of  milk  and  butter  by  onions, 
fish,  or  other  kinds  of  food,  if  they  are  kept  in  the  same  com- 
partment of  a  refrigerator.  Onions,  for  instance,  give  off  a 
small  quantity  of  gas  which  we  can  easily  detect  by  our  sense 
of  smell,  or  by  the  watering  of  our  eyes.  This  gas,  when 
absorbed  by  milk  or  butter,  affects  its  taste. 

106.  Diffusion  of  gases.     The  diffusion  of  hydrogen  through 
a  porous  cup  is  shown  in  the  following  experiment. 

If  we  set  up  a  porous  cup  with  a  stopper  and  glass  tube,  as  shown  in 
figure  134,  and  allow  hydrogen  (or  illuminating  gas)  to  fill  the  jar  which 
surrounds  the  porous  cup,  we  observe  bubbles  rising  from  the  end  of  the 
glass  tube,  which  dips  under  water.  This  means  that  the  gas  is  going 
through  the  porous  walls  of  the  cup  and  forcing  the  air  out  at  the  bot- 
tom. If  we  now  shut  off  the  gas  and  remove  the  jar,  we  presently  see 
the  water  slowly  rising  in  the  tube ;  this  shows  that  the  gas  inside  the 
cup  is  going  out. 

The  fact  that  a  little  ammonia  (or  any  other  gas  with  a 
powerful  odor)  introduced  into  a  room  is  soon  perceptible  in 


MOLECULAR   THEORY  OF  GASES 


125 


Porous  cup 
Glass  beaker 
*? 


every  part  of  the  room  shows  that  the  gas  particles  travel 
quickly  across  the  room.  Moreover,  this  mixing  of  gases 
goes  on,  whatever  the  relative  densities  of  the  gases ;  so  that 
a  heavy  gas  like  carbon  dioxide  and 
a  light  gas  like  hydrogen  will  not 
remain  in  layers  like  mercury  and 
water,  but  will  quickly  diffuse  and 
become  a  homogeneous  mixture.  Ex- 
periments show  that  the  smaller  the 
density  of  the  gas,  the  greater  the 
velocity  of  its  diffusion.  This  is  the 
basis  of  a  process  recently  proposed 
for  separating  helium  from  natural 
gas  by  successive  selective  diffusions. 

107.  Molecular  theory  of  gases. 
To  explain  the  pressure  of  gases  and 
their  diffusion,  it  is  now  generally 
believed  that  all  substances  consist 
of  very  minute  particles  called  mole- 
cules. These  molecules  are  so  minute  that  we  cannot  see 
them  even  with  the  most  powerful  microscopes.  In  one  cubic 
centimeter  of  a  gas  there  are  not  less  than  25  X  1018  (that 
is,  25  followed  by  18  ciphers)  molecules.  The  spaces  between 
the  molecules  are  much  larger  than  the  molecules  themselves. 
This  explains  why  gases  are  so  easily  compressed  and  diffuse 
so  quickly. 

Then,  too,  these  little  particles  are  flying  about  in  all  directions 
with  great  velocity.  They  travel  in  straight  lines  except  when 
they  hit  each  other  and  bounce  off.  Gas  molecules  seem 
to  have  no  inherent  tendency  to  stay  in  one  place,  as  do  the 
molecules  of  solids.  This  explains  why  gases  fill  the  whole 
interior  of  a  containing  vessel.  This  also  explains  gas  pres- 
sures, for  the  blows  which  the  innumerable  molecules  of  a 
gas  strike  against  the  surrounding  walls  constitute  a  con- 
tinuous force  tending  to  push  out  these  walls.  When  a 


Fig.  134.     Diffusion  of  hydro- 
gen through  porous  cup. 


126  MECHANICS  OF  GASES 

I 

gas  is  compressed  to  half  its  volume,  the  pressure  is  doubled, 
because  doubling  the  density  doubles  the  number  of  blows 
struck  per  second  against  the  walls.  It  has  even  been  possible 
to  calculate  the  molecular  velocity  necessary  to  produce  this 
outward  pressure.  It  appears  that  the  molecules  of  gases 
under  ordinary  conditions  are  traveling  at  speeds  between  1 
and  7  miles  per  second.  The  speed  of  a  cannon  ball  is  seldom 
greater  than  one  half  a  mile  per  second. 

This,  in  brief,  is  the  so-called  kinetic  theory  of  gases. 

SUMMARY  OF  PRINCIPLES  IN  CHAPTER  IV 

Atmospheric  pressure  is  equal  to  about 

30  inches  of  mercury, 
34  feet  of  water, 
15  pounds  per  square  inch, 
1  kilogram  per  square  centimeter. 

Lifting  effect  of  air  is  equal  to  weight  of  air  displaced. 

Total  lift  of  a  balloon  equals  difference  between  weight  of  gas 
and  weight  of  air  displaced. 

Pascal's  Law  of  Transmission  of  Pressure :  For  gases  under 
pressure,  the  pressure  is  transmitted  undiminished  in  all 
directions ;  the  force  varies  as  the  area. 

Boyle's  Law:   At  constant  temperature  the  volume  of  a  gas 
varies  inversely  as  the  pressure. 
The  density  of  a  gas  varies  directly  as  the  pressure. 

QUESTIONS 

1.  How  much  of  a  vacuum  can  one  suck  with  one's  mouth?    How 
hard  can  one  blow? 

2.  How  and  why  can  a  glass  of  water  be  inverted  with  the  aid  of  a 
card  without  spilling  the  water  ? 

3.  What  would  be  the  result  of  putting  a  mercurial  barometer  under 
a  tall  bell  glass  on  a  vacuum  pump? 


QUESTIONS  ON  GASES 


127 


4.  What  would  be  the  effect  of  lengthening  the  long  arm  of  a 
siphon  ? 

5.  A  boat  lying  on  a  beach  is  full  of  water.     How  could  you  empty 
it  with  the  help  of  a   suitable  length  of  hose? 

Could  you  use  the  same  method  to  get  the  bilge 
water  out  of  a  boat  floating  in  the  water  ? 

6.  Figure  135  shows  a  gauge  which  may  be 
attached  to  the  tube  of  an  automobile  or  bicycle 
tire  to  measure  the  pressure  of  the  compressed  air. 
Explain  its  operation. 

7.  Explain  why  the  liquid  does  not  run  out  of  a 
medicine  dropper. 

8.  Explain  the  action  of  a  drinking  fountain 
(Fig.  136). 

9.  A  man  finds  that  vinegar  does  not  flow  out 
of  a  barrel  until  he  removes  the  bung.     Explain. 

10.  A  vessel  one  meter  deep  is  filled  with  mer- 
cury.    Can  it  be  entirely  emptied  by  means  of  a 
siphon  ? 

11 .  Why  does  a  man  in  a  diving  suit  under  water 
have  to  be  supplied  with  compressed  air  ? 


T 


Fig.  135.  Pressure 
gauge  used  for 
automobile  tires. 


12.  What   advantages   has   compressed   air 
over  electricity  for  the  transmission  of  power? 

13.  If  the  area  of  a  man's  body  is  20  square 
feet,  what  is  the  total  force  exerted  on  him  by 
the  atmosphere?     Why  is  he  not  crushed  by 
this  force  ? 

14.  In  building   tunnels    workmen    usually 
have  to  work  in  chambers   filled  with   com- 
pressed air.     Why  is  this  necessary  ? 

15.  What  facts  indicate  that  the  atmosphere 
becomes  rarer  and  rarer  as  one  rises  above  sea 
level? 

16.  How  can  a  balloon  be  made  to  sink  or  rise  ? 


Fig.  136.     Drinking 
fountain. 


17.    If  a  balloon  is  full  of  hydrogen  when  it 
leaves  the  ground,  why  does  it  not  burst  when 
it  rises  into  a  region  of  lowered  atmospheric  pressure? 


128 


MECHANICS  OF  GASES 


18.  Why  does  a  trailing  drag-rope  make  it  easier  to  land  a  free 
balloon  gently? 

19.  How  does  a  gas  meter  (Fig.  137)  work  ? 


FEET 


CUBIC 


FEET 


Fig.  137.     Diagram  of  a 
gas  meter. 


Fig.  138.     Dials  on  a  gas  meter. 


20.  Figure  138  represents  the  dials  on  a  gas  meter  at  the  beginning 
and  at  the  end  of  the  month,   (a)  What  is  the  purpose  of  the  small 
dial  marked  Two  Feet?  (6)  If  gas  costs  $1.25  per  1000  cubic  feet, 
what  is  the  amount  of  the  bill  for  the  month?   (c)  Draw  a  diagram 
to  represent  84,600  cubic  feet. 

21.  Would  it  make  any  difference  in  the  gas  bill  if  the  meter  were 
in  the  attic  instead  of  in  the  cellar?     In  apartment  houses  with  a 
separate  meter  for  each  apartment,  do  the  people  on  the  top  floor  get 
more  or  less  gas  for  their  money? 

22.  A  city  gas  plant  stands  in  a  valley  and  a  gas  main  runs  from  it 
to  a  house  high  on  a  hill  above  it.   'Will  the  gas  pressure  in  the  main, 
as  measured  by  a  manometer  (Fig.  131),  be  greater  at  the  gas  works  or 
at  the  house?     Why? 


CHAPTER  V 


NON-PARALLEL  FORCES 

Representation  of  forces  by  arrows  —  the  parallelogram  of 
forces  —  composition  and  resolution  of  forces  —  finding  coeffi- 
cient of  friction  —  application  to  roof  truss,  sailboat,  and  air- 
plane. 

108.  Three  forces  acting  at  a  point.  In  machines  and  other 
contrivances  it  often  happens  that  forces  which  are  not  par- 
allel balance  each  other  and 
are  thus  in  equilibrium. 
For  example,  suppose  a 
street  lamp  is  suspended 
over  a  street  by  a  wire 
stretched  between  two  posts, 
as  shown  in  figure  139. 
We  have  here  three  non- 
parallel  forces  in  equili- 


Fig.  139.     Three  non-parallel  forces. 


brium:  first,  the  vertical  pull  OW  due  to  the  weight  of  the 
lamp ;  second,  the  pull  exerted  by  one  of  the  ropes  OA ;  and 
third,  the  pull  exerted  by  the  other  rope  OB.  We  are  now 
to  find  what  relation  must  exist  between  the  magnitude  and 
direction  of  any  three  such  forces,  in  order  that  they  may  pro- 
duce equilibrium. 

109.  Representation  of  forces  by  arrows.  It  will  help  us  to 
form  a  mental  picture  of  these  three  forces  if  we  represent  each 
of  them  by  an  arrow.  The  direction  of  each  force  will  be 
indicated  by  the  direction  of  the  arrow,  the  point  of  applica- 
tion by  the  tail  of  the  arrow,  and  the  magnitude  of  the  force 
by  the  length  of  the  arrow,  drawn  to  some  convenient  scale. 

129 


130 


NON-PARALLEL  FORCES 


Thus,  in  figure  140  we  have  an  arrow  3  units  long,  and  if  we 

assume  that  each  unit  represents  10  pounds,  the  arrow  OX 

,       j       j  represents  a  force  of  30  pounds  applied  at  0, 

x       acting  due  east.     Figure  141  represents  two 

Fig.  140.    A  force  of  forces,  one  OX  of  30  pounds,  acting  due 

30  pounds  acting  east.  e 

east  applied  at  0,  and  the  other  OF  of  40 
pounds,  acting  due  north,  applied  at  the  same  point  0. 

If  these  two  forces  act  simultaneously  upon  the  body  at  0, 
the  result  will  be  the  same  as  if  a  single  force 
were  applied,  acting  somewhere  between  OX 
and  OF,  but  nearer  the  greater  force  0  F. 
This  single  force  OR,  which  produces  the  same 
result  as  two  forces  OX  and  OF,  is  called  their 
resultant. 

110.  Principle  of  parallelogram  of  forces. 
If  a  parallelogram  is  constructed  on  OX  and 
0  Y,  the  diagonal  OR  represents  the  resultant.  Fig.  141.  Resuit- 
This  can  be  illustrated  by  the  following  ex-  atntri°ght™  gieTS 
periment. 

Suppose  we  hang  two  spring  balances  A  and  B  from  two  nails  in  the 

molding  at  the  top  of  a  black- 
board, as  shown  in  figure  142, 
and  tie  some  known  weight  W 
near  the  middle  of  a  string 
joining  the  hooks  of  the  two 
balances.  If  we  draw  a  line 
on  the  blackboard  behind  each 
of  the  three  strings,  we  shall 
have  represented  the  direction 
of  each  of  the  three  forces. 
Then  we  note  the  tension  in 
each  string,  as  shown  by  t1  , 
amount  of  the  weight  W  ,L> 
the  readings  of  the  spring  bal- 
ances A  and  B,  remove  the 
apparatus,  and  complete  the 
Fig.  142.  Ezperiment  to  illustrate  paral-  diagram.  Choosing  some  con- 


lelogram  law. 


venient  scale,  we  measure  off 


RESULTANT  DEPENDS  ON  THE  ANGLE 


131 


on  OA  a  distance  corresponding  to  the  tension  in  OA,  and  place  an 
arrowhead  at  X;  in  the  same  way  we  locate  Y  on  OB.  Then  we  con- 
struct a  parallelogram  on  OX  and  OF  by  drawing  XR  parallel  to  OF 
and  YR  parallel  to  OX.  It  is  evident  that  the  diagonal  OR  is  the 
resultant  of  OX  and  OF,  for  if  we  measure  OR  and  determine  its 
magnitude  from  our  scale  of  force,  we  find  that  this  resultant  OR  is 
almost  exactly  equal  and  opposite  to  the  third  force  OW.  That  is,  OW  is 
balanced  by  OR  or  by  OX  and  OF. 

The  force  necessary  to  balance,  or  hold  in  equilibrium,  two 
forces  is  called  the  equilibrant.  Thus,  in  the  case  just  de- 
scribed, the  force  OW  is  the  equilibrant  of  the  two  forces  OX 
and  0  F. 

The  resultant  of  two  forces  acting  at  any  jangle  may  be  rep- 
\  resented  by  the  diagonal  of  a  parallelogram'  constructed  on  two 
\rrows  representing  the  two  forces. 

vPhen  three  forces  are  in  equilibrium,  the  resultant  of  any 
two  of  the  forces  is  equal  and  opposite  to  the  third,  which  can 
be  regarded  as  their  equilibrant.  / 

111.  Resultant  depends  on  the  angle  between  forces.  To 
determine  ibhe  resultant  of  ;two  or  more  forces,  we  must  know 


(c)  (d) 

Fig.  143.     Two  forces  at  varying  angles. 


(e) 


not  only  their  magnitudes,  but  also  the  angle  between  them. 
This  will  be  made  clear  by  studying  the  same  two  forces  at 
different  angles,  as  in  figure  143.  It  will  be  seen  that  the 
resultant  OR  gradually  increases  as  the  angle  between  the 
forces  OX  and  OY  decreases  from  180°  to  0°. 

FOR  EXAMPLE,  if  the  angle  is  180°  as  in  (a),  the  forces  OX  and  OF  are 
opposite,  and  the  resultant  is  the  difference  between  the  forces,  4  —  3, 
or  1,  and  acts  in  the  direction  of  the  greater  force,  i.e.  toward  the  right. 
As  the  angle  gradually  decreases  the  resultant  OR  increases,  until, 


132 


NON-PARALLEL  FORCES 


when  the  angle  is  0°  as  in  (e),  the  forces  OX  and  OY  are  acting  in  the 
same  straight  line  and  in  the  same  direction,  and  the  resultant  is  the 
sum  of  the  two  forces,  4  +  3,  or  7.  When  the  forces  are  at  right  angles 
as  in  (c),  the  resultant  can  be  computed  from  the  geometrical  propo- 
sition about  the  sides  of  a  right  triangle,  namely,  the  square  on  the 
hypothenuse  is  equal  to  the  sum  of  the  squares  on  the  two  sides. 


Thus, 


07?  =  OX*  +  OY2 
Otf=  32  +  42  =  25 
OR  =  5. 


For  oblique  angles,  such  as  (6)  and  (d)  in  figure  143,  the  resultant 
can  be  determined  by  plotting  the  forces  to  scale,  or  by  trigonometry. 

The  process  of  finding  the  resultant  of  two  or  more  com- 
ponent forces  is  called  the  composition  of  forces. 


112.  Illustrative  examples  of  composition  of  forces, 
a  crane  arm  AB  attached   to 


w 


Fig.  144.     Three  forces  acting  on  a  crane. 
A  W  form  a  right  angle,  we  know  that 


Suppose  we  have 

wall  as  shown  in  figure  144  (a). 
E  The  weight  W  is  2000  pounds 
and  the  tension  in  the  cable  A  C 
is  1500  pounds.  What  is  the 
force  exerted  by  AB?  In  the 
solution  of  such  problems  it  will 
be  found  helpful  to  draw  a  force 
diagram  (Fig.  144  (6) ),  where 
AW  represents  the  pull  of  the 
weight  W,  AC  the  pull  of  the 
cable,  and  AE  the  thrust  of 
the  crane  arm.  As  these  three 
forces  are  in  equilibrium,  we 
can  apply  the  principle  of  the 
parallelogram  of  forces.  We 
want  to  find  AR,  the  resultant 
of  A  C  and  A  W.  Since  A  C  and 


A  tf 


or 


,+  AW*  =  15002  +  20002 
AE  =  2500  pounds. 


Therefore  the  push  exerted  by  A  B  is  2500  pounds. 


RESOLUTION  OF  FORCES 


133 


Again,  suppose  we  have  a  100-pound 
child  in  a  swing  (Fig.  145).  A  man  pushes 
the  child  to  one  side  with  a  force  of  20 
pounds.  What  are  the  magnitude  and  direc- 
tion of  the  pull  exerted  by  the  rope  ?  In  the 
force  diagram  (Fig.  145),  CW  represents 
the  weight  of  the  child  (100  pounds),  CP 
represents  the  push  (20  pounds)  of  the 
man  against  the  child,  and  CR  repre- 
sents the  pull  of  the  rope  which  we 
wish  to  determine.  The  resultant  CR' 
of  CP  and  CW  is  equal  to  VCP*  +  CW*, 
or  \^(20)2  +  (100)2,  or  about  102  pounds. 
Therefore  the  tension  in  the  rope  is  also 
102  pounds.  Its  direction  can  be  found 
from  the  diagram. 


w 


Fig.  145.     Three  forces  act- 
ing on  child  in  swing. 


PROBLEMS 

(In  the  following  problems  first  solve  by  plotting  on  as  large  a  scale  as  possible 
and  then  by  computation.) 

1.  Find  the  resultant  of  a  force  of  8  pounds  toward  the  east  and  one 
of  4  pounds  toward  the  north. 

2.  A  force  of  100  pounds  acts  north  and  an  equal  force  acts  west. 
What  is  the  direction  and  magnitude  of  the  equilibrant  ? 

3.  Find  the  resultant  of  a  force  of  10  pounds  east  and  one  of  14.1 
pounds  southwest. 

4.  Two  100-pound  forces  act  at  an  angle  of  60°  with  each  other. 
Find  their  resultant. 

6.    Find  the  resultant  of  two  100-pound  forces  which  act  at  an  angle 
of  120°  with  each  other. 

6.  Two  forces,  5  pounds  and  12  pounds,  act  at  the  same  point.     Find 
their  equilibrant,  (a)  if  they  act  in  the  same  direction ;  (6)  if  they  act  in 
opposite  directions ;  and  (c)  if  they  act  at  right  angles. 

7.  Find  the  resultant  of  three  forces:    A   10  pounds  north,  B  15 
pounds  south,  and  C  12  pounds  west.     (First  find  the  resultant  of  A 
and  B  and  then  the  resultant  of  this  resultant  and  C.) 

113.   Resolution  of  forces.     The  principle  of  the  composi- 
tion of  forces  can  be  worked  backward.     If  one  force  is  given, 


134 


NON-PARALLEL   FORCES 


Fig.  146. 


Diagram  of  three  forces  acting  on 
street  lamp. 


we  can  find  two  others  in  given  directions  which  will  balance 
it.  For  example,  take  the  case  of  the  lamp  suspended  above 
the  middle  of  the  street  (Fig.  139).  If  we  know  the  weight 
of  the  lamp  and  the  angle  of  sag  of  the  ropes,  we  can  calculate 
the  tension  in  the  ropes. 

FOR  EXAMPLE,  suppose  that  the  weight  of  the  lamp  is  50  pounds,  and 
that  the  rope  ALB  (Fig.  146)  sags  so  as  to  make  both  the  angle  ALR 

and  the  angle  BLR  equal  to 
75°.  In  the  diagram  draw 
the  arrow  LW  down  from  L 
to  represent  50  pounds  on 
some  convenient  scale.  As 
the  two  ropes  have  to  hold 
up  the  lamp,  the  resultant  of 
the  forces  representing  the 
tension  in  the  ropes  must  be 
l  and  opposite  to  the 
H 
force  representing  the  weight. 

So  we  draw  LR  equal  and  opposite  to  LW.  Then  we  construct  a 
parallelogram  on  LR  as  a  diagonal  with  its  sides  parallel  to  LA  and 
LB,  Ry  being  drawn  parallel  to  LA,  and  Rx  parallel  to  LB.  Ly  repre- 
sents the  tension  in  the  rope  LB  and  is  found  by  measurement  to  be 
equal  to  about  96.6  pounds,  and  Lx  represents  the  tension  in  LA  and 
is  also  equal  to  about  96.6  pounds. 

Another  good  example  of  the  resolution  of  one  force  into  two 
forces  which  just  balance  it  is  the  case  of  a  street  lamp  hung 
out  on  a  bracket  from  a  pole,  as  shown  in  figure  147  (a). 

FOR  EXAMPLE,  suppose  the  lamp  L,  weighing  50  pounds,  is  hung  out 
from  a  pole  PC  by  means  of  a  stiff  rod  A  B,  10  feet  long,  and  a  tie  rope 
or  wire  BC,  which  is  fastened  to  the  pole  at  C,  3  feet  above  A.  What 
is  the  force  exerted  by  the  rope  BC? 

In  the  diagram  (Fig.  147  (6)  ),  the  weight  of  the  lamp  is  represented 
by  OW,  the  push  of  the  rod  AB  by  OP,  and  the  tension  of  the  tie  rope 
BC  by  OT.  Since  we  know  the  force  OW  (50  pounds),  we  draw  this 
line  to  some  convenient  scale.  The  resultant  of  OP  and  OT  must  be 
equal  and  opposite  to  OW.  Therefore  we  make  OR  equal  and  opposite 
to  OW.  Then,  completing  a  parallelogram  on  0 R  as  a  diagonal,  we 
have  OP  representing  the  push  of  the  rod  against  the  lamp,  and  0  T  the 


COMPONENT  IN  A  GIVEN  DIRECTION 


135 


tension  in  the  tie  rope  BC.     If  we  draw  these  lines  carefully  to  scale, 
we  find  that  the  tension  is  174  pounds.     How  much  is  the  push  OP? 

In  general,  a   single  force  may  be  resolved   into  two  forces 
acting  in  given  directions,  by  constructing  a  parallelogram  whose 


50  lb. 


Fig.  147.     Three  forces  acting  on  lamp  hung  in  bracket. 

diagonal   represents  the  given  force,  and   whose  sides   have  the 
given  directions. 

114.  Component  of  a  force  in  a  given  direction.  If  a  force 
is  given,  we  can  find  two  other  forces,  one  of  which  repre- 
sents the  whole  effect  in  a  given  direction  of  the  given  force. 

Thus  in  figure  148  we  have  a  canal  boat  AB  which  is  be- 
ing towed  by  the  rope  BC.  We  may  resolve  the  force  along 


Fig.  148.     Useful  component  of  force  acting  on  canal  boat. 


the  rope  BC  into  two  forces,  one  of  which,  BE,  is  effective  in 
pulling  the  boat  along  the  canal,  and  the  other,  BD,  at  right 
angles,  is  useless  or  worse  than  useless,  since  it  tends  to  pull 
the  boat  toward  the  bank.  BE,  the  useful  component  of 
BC,  can  be  computed  by  drawing  the  force  BC  to  scale  and 
then  constructing  a  rectangle  on  BC  as  a  diagonal,  such  as 
BECD. 


136  NON-PARALLEL   FORCES 

115.  Hints  on  solving  practical  problems.  The  principle 
of  the  parallelogram  of  forces  is  one  of  the  foundation  stones 
in  the  study  of  mechanics.  When  stated  with  the  aid  of  a 
geometrical  diagram,  it  seems  simple,  but  when  met  with  in 
a  crane,  derrick,  bridge,  or  roof  truss,  it  is  puzzling.  This  is 
because,  in  solving  practical  problems,  we  seldom  find  bodies 
which  are  small  enough  to  be  regarded  as  points  at  which 
forces  act.  Nevertheless  we  can  solve  problems  by  this  method, 
even  when  the  bodies  are  large.  For  if  any  body  is  held  still 

by  three  forces, 
their  lines  of  ac- 
tion, if  prolonged, 
must  go  through 
'B  a  single  point,  as 
shown  in  (a),  fig- 

Condition  of  spin  and  rest.  Ur<?    149'       If    th'S 

were  not  true  of 
three  forces  acting  on  a  body  (Fig.  120  (6)  ),  it  would  spin 
around.  So  we  can  think  of  the  forces  as  acting  at  a  single 
point,  even  though  the  body  in  which  the  point  lies  is  large. 

Another  difficulty  in  solving  practical  problems  is  the  fail- 
ure to  visualize  all  the  forces  (pushes  or  pulls)  acting  on  any 
body.  A  beam  may  be  pushing  or  a  rod  may  be  pulling, 
even  though  it  does  not  move.  Experience  shows  that  it 
is  helpful  to  draw  two  diagrams,  side  by  side.  One  should 
be  a  sketch  of  the  .body  by  itself,  isolated  from  its  surround- 
ings. This  sketch  should  show  dimensions,  angles,  and  the 
directions  and  points  of  application  of  all  the  forces  acting 
on  the  body.  Do  not  consider  any  forces  which  the  body  may 
itself  be  exerting  .on  anything  else.  Also,  do  not  forget  the 
weight  of  the  body.  The  second  diagram  shows  only  the 
forces  themselves,  each  represented  by  an  arrow  drawn  to 
scale  starting  from  a  common  origin,  and  such  construction 
lines  as  may  be  necessary  to  form  the  needed  parallelograms 
and  resultants. 


FRICTION  ON  AN  INCLINED   PLANE 


137 


APPLICATIONS  OF  THE  PARALLELOGRAM  OF  FORCES 
116.  Friction  on  an  inclined  plane.  When  an  object  is 
placed  on  an  inclined  plane,  friction  tends  to  keep  the  object 
from  sliding  down  the  plane  (Fig.  150).  If  the  angle  of  in- 
clination is  small  enough,  this  friction  will  prevent  the  object 
from  sliding  down  the  plane. 

FOR  EXAMPLE,  suppose  an  electric  car  is  on  a  grade  with  the  brakes  set 
so  that  the  car  stands  still.  How  steep  can  the  grade  be  before  the  car 
slides  down?  In  the  diagram,  figure  150,  let  OW  represent  the  weight 
of  the  car,  OP  the 
pressure  of  the  inclined 
plane  against  the  car, 
and  OF  the  friction 
which  retards  its  mo- 
tion. When  these  three 
forces  are  in  equilib- 
rium, the  resultant 
of  OP  and  OW,  that 
is,  OR,  must  be  op- 


Fig.  150.     Friction  on  inclined  plane. 


posed  by  an  equal  force  OF.  Now  OF  can  never  exceed  a  limiting  value 
which  depends  on  the  pressure  and  on  the  coefficient  of  friction,  the 
latter  being  determined  by  the  condition  of  the  track.  But  the  result- 
ant OR  increases  as  the  incline  becomes  steeper.  So,  as  the  steepness 
increases,  we  soon  reach  a  condition  in  which  OR  is  greater  than  OF 
possibly  can  be,  and  the  car  slides  down.  If  we  know  the  coefficient 
of  friction  between  the  wheels  and  the  rails,  we  can  compute  the  grade 
at  which  the  car  will  begin  to  slide. 

Let  figure  150  represent  this  grade.  We  have  already  (section  52) 
defined  the  coefficient  of  friction  as  the  ratio  between  friction  and  pres- 
sure, and  so,  in  this  case,  we  have 

Coefficient  of  friction  =  g^  =  ||. 

From  geometry  we  know  that  the  triangles  OPR  and  XYZ  are  similar 
since  they  are  mutually  equiangular.     It  follows  that 
OR  _  H_  _  height  of  plane 
OP      B         base  of  plane  ' 
Therefore 

height  of  plane 
base   of  plane 
This  is  a  convenient  way  of  measuring  coefficients  of  friction. 


Coefficient  of  friction 


138 


NON-PARALLEL  FORCES 


PROBLEMS 

(Solve  these  problems  by  means  of  large,  carefully  made  diagrams,  and  check 
your  answers,  whenever  you  can,  by  computation.) 

1.    Given  a  force  of  100  pounds  acting  north.     Resolve  this  into  two 
forces,  one  acting  northeast  and  the  other  northwest. 

2.  Given  a  force   of    100 
pounds  acting  north.  Resolve 
this  into  two  forces,  one  act- 
ing northwest  and  the  other 
east. 

3.  Given  a   force  of   100 
pounds  acting  north.  Resolve 
this  into  two  forces  acting  at 
right  angles  with  each  other, 
one  of  which  shall  be  twice 
as  great  as  the  other. 

4.  A   man    pushes    on    a 
lawn  mower  (Fig.  151)  with 
a  force  of  60  pounds  along 

the  handle,  which  is   tilted  at  an  angle  of  30°  from  the   ground, 
(a)  What  is  the  useful  component  of  this  force  ?  (6)  If  the  handle  is 
tilted  at  an  angle  of  45°,  what 
is  the  useful  component  ? 

6.  A  200-pound  barrel  of 
flour  is  held  in  place  on  a 
skid  (Fig.  152).  If  the  skid 
is  so  tilted  as  to  make  an 
angle  of  30°  with  the  ground, 

(a)  what  force  must  a  man 
exert  parallel  to  the  incline? 

(b)  What  force  does  the  skid 
exert    (perpendicularly)   on 
the  barrel? 


Fig.  151. 


Useful  component  of  push  against 
lawn  mower. 


N 


Fig.  152.     Forces  applied  to  barrel  on  skid. 


117.  Roof  truss.  When  a  wooden  house  is  built,  the  roof 
is  usually  supported  by  pairs  of  timbers  set  like  an  inverted 
V,  as  in  figure  153.  Each  pair  of  timbers  has  to  carry  the 
weight  of  a  section  of  the  roof,  and,  in  winter,  of  the  snow 
and  ice  that  accumulate  on  it.  This  weight  is  really  dis- 


ROOF   TRUSS 


139 


tributed  along  the  timbers;  but  it  can  be  thought  of  as  con- 
centrated, half  at  the  peak  and  half  at  the  eaves,  where  it- 
rests  directly  on  the  walls. 
The  part  of  the  load  that 
is  at  the  peak  tends  to 
"  spread  "  the  inverted  V, 
and  our  problem  is  to  find 
what  has  to  be  done  to 
prevent  this. 


Fig.  153. 


m 

Roof  trusses. 


We  may  test  this  experi- 
mentally with  a  small  model 
of  a  pair  of  roof  trusses  (Fig. 
154).  These  have  hinges  at  the  top  instead  of  a  stiff  joint,  and 
frictionless  wheels  underneath,  so  that  they  will  not  stand  up  at  all 
under  the  load  W  unless  a  tie  is  put  across  the  bottom  of  the  A  to  prevent 
the  spreading.  If  a  spring  balance  is  put  into  the  tie,  the  pull  which  the 
tie  has  to  exert  on  the  truss  members  can  be  measured.  If  the  load  at 


(b) 
Fig.  154.     Experimental  roof  truss  and  force  diagram. 


the  peak  is  50  pounds,  and  if  the  truss  members  make  a  right  angle,  the 
"  tension  "  in  the  tie  will  be  about  25  pounds. 

In  discussing  this  experiment,  we  have  to  apply  the  parallelogram  of 
forces  at  two  points  successively.  In  the  first  place,  let  us  consider  the 
pin  A  of  the  hinge  at  the  top.  This  is  acted  on  by  three  forces,  the  pull 
of  the  weight  A  W,  and  the  push  exerted  by  each  rod  AB  and  AC 
(Fig.  154(6)).  Since  these  balance,  we  can  find  each  push  by  construct- 
ing a  parallelogram  whose  diagonal  is  equal  and  opposite  to  A  W.  If  the 
rods  are  at  right  angles,  this  parallelogram  is  a  square,  and  the  pushes 
are  equal.  Let  each  push  =  x,  then  2  x2  =  50 2,  or  x  =  35.3  pounds. 


140 


NON-PARALLEL   FORCES 


Turning  next  to  the  pin  at  the  foot  of  one  rod,  we  see  that  it  is  also 
acted  on  by  three  forces,  the  push  of  the  rod,  35.3  pounds,  the  upward 
push  exerted  by  the  table  which  is  ^W  (half  the  weight),  and  the 
pull  of  the  tie  wire.  Since  these  balance,  we  can  get  the  last  by  con- 
structing the  diagonal  of  a  parallelogram  on  the  known  forces.  This 
parallelogram  is  composed  of  two  45°  triangles,  and  so  the  pull  of  the 
tie  wire  equals  the  push  of  the  table,  or  25  pounds. 

In  building  a  roof,  the  pull  exerted  by  the  tie  wire  in  our 
experiment  has  to  be  provided  for  in  some  way.  Usually 
the  ends  of  the  roof  timbers  are  nailed  to  the  frame  of  the 
building,  which  is  stiff  enough  to  exert  a  part  or  all  of  the 


Framed  bridge  with  pinned  joints. 


required  force.  Often  a  board  is  nailed  across  the  inverted 
V,  either  at  the  bottom  or  a  little  higher  up,  to  help  exert  it. 
In  large  roof  trusses,  as  in  churches,  an  iron  rod  is  strung 
across  and  tightened  with  a  screw  coupling. 

118.  Bridges.  Large  bridges  are  built  of  wood  or  steel 
"members"  joined  to  form  a  number  of  adjacent  triangles. 
If  the  members  are  strong  enough  not  to  stretch,  shorten,  or 
buckle  under  the  loads  imposed  on  them,  each  triangle,  having 
three  sides  of  unchanging  length,  keeps  its  shape,  and  so  the 
whole  truss  is  rigid, 


HOW  A   BOAT  SAILS  INTO   THE   WIND 


141 


In  very  large  bridges  the  members  are  joined  together  at  the  corners 
of  the  triangles  by  boring  holes  in  them  and  thrusting  a  steel  pin  through 
all  the  holes  at  a  joint.  Bridges  made  in  this  way  are  called  pinned 
bridges  (see  Fig.  155).  In  designing  a  pinned  bridge,  an  engineer 
computes  the  "stresses  in  the  members,"  that  is,  the  forces  which  they 
have  to  exert  to  hold  the  - 
bridge  stiff  under  load,  by 
applying  the  parallelogram 
of  forces  to  the  pin  at  each 


Fis-   I56. 


Diagram    of    the 
in  figure  155. 


bridge    shown 


joint  successively.  The 
members  which  have  to 
push  against  the  pins  at 
their  ends  are  called  com- 
pression members,  because  they  tend  to  shorten  under  load;  while 
those  that  have  to  pull  on  the  pins  at  their  ends  are  tension  members, 
and  tend  to  lengthen  under  load.  In  large  bridges  it  is  easy  to  see 
which  are  compression  members  and  which  tension,  for  the  compression 
members  are  made  broad  and  stiff  with  "  latticing  "  up  their  sides,  while 

the  tension  members  are  steel 
straps  or  rods  with  enlarged  ends 
to  give  room  for  the  holes.  Thus 
the  heavy  lines  in  figure  156  indi- 
cate compression  members,  while 
the  light  lines  correspond  to  ten- 
sion members. 

In  smaller  bridges  the  members 
are  not  joined  by  pins,  but  are 
riveted  to  "  gusset  plates  "  at  each 
joint.  Such  bridges  are  designed 
as  if  they  were  pinned,  the  stiff 
joints  giving  an  additional  factor 
of  safety. 

The  smallest  steel  bridges  are 
supported  by  plate  girders,  one 
the  on  each  side,  which  are  simply  stiff 
steel  beams.  Roofs  of  large  span 
are  often  supported  by  framed  trusses,  made  of  members  forming 
triangles,  like  bridge  trusses. 

119.  How  a  boat  sails  into  the  wind.  Let  figure  157  repre- 
sent a  boat,  SSf  its  sail,  and  W  the  wind.  It  is  sometimes 
hard  to  see  how  such  a  wind  pushes  the  boat  ahead  instead 


Fig.   157. 


How  a  boat  sails  into 
wind. 


142  NON-PARALLEL  FORCES 

of  forcing  it  backward.  The  wind  blowing  against  the  slanting 
sail  SS'  is  deflected  and  causes  a  force  perpendicular  to  the 
surface.  This  force  can  be  represented  by  the  arrow  CP  in  the 
diagram.  The  force  CP  can  be  resolved  into  two  compo- 
nents: one  useful,  CF,  which  points  forward  parallel  to  the 
keel  of  the  boat ;  and  the  other  useless,  CL,  which  tends 
to  move  the  boat  to  leeward.  This  sidewise  movement  is 
largely  prevented  by  a  deep  keel  or  a  center  board.  So  the 
net  effect  of  the  wind  is  to  drive  the  boat  forward. 

120.   Airplanes  and  seaplanes.     The  "  first  successful  power 
flight  in  the  history  of  the  world  "  was  made  on  the  morning 


Fig.  158.     Front  view  of  the   Martin  mail-carrying  biplane  with  two  motors. 

of  December  17,  1903,  by  the  Wright  brothers.  Since  that 
date,  the  flying  machine  has  been  so  perfected  as  to  become 
a  powerful  weapon  in  war,  a  valuable  scouting  machine  for 
locating  forest  fires  and  schools  of  fish  at  sea,  and  an  increas- 
ingly useful  means  of  commercial  transportation.  Mails  go 
by  airplane,  and  there  is  a  network  of  regular  daily  air  services 
all  over  Europe,  those  between  London  and  Paris  carrying 
over  1000  passengers  in  a  single  month  in  1921. 

The  biplane  (Fig.  158)  is  the  prevailing  type;    it  has  two 
wings  set  one  above  the  other.     Each  wing  is  long  and  narrow 


AIRPLANES 


143 


and  moves  with  its  long  edge  forward,  as  this  shape  and  aspect 
have  been  found  to  give  much  more  lift  per  square  foot  than 
any  other.  Large  monoplanes,  with  a  single  wing  on  each 
side  of  the  body,  are  apparently  the  coming  type.  Their 
wings  are  thick  enough  to  allow  internal  bracing  exclusively 
and  are  sometimes  covered  with  thin  sheets  of  metal  instead 
of  the  prevailing  cloth  fabric. 

The  propellers  are  driven  by  light  but  very  powerful  gasoline 
engines,  such  as  the  American  Liberty  motor  (Fig.  159),  either 


Fig.  159.     The  Liberty  motor  was  developed  during  the  World  War. 
806  pounds  and  is  rated  at  400  horse  power. 


It  weighs 


directly  or  through  speed-reducing  gears.  In  the  smaller 
planes  there  is  one  propeller,  usually  in  front,  where  it  pulls 
the  plane  along.  The  larger  planes  have  two,  three,  or  even  four 
engines,  each  driving  a  propeller. 

Airplanes  have  two  or  more  wheels  underneath  so  that  they 


144 


NON-PARALLEL  FORCES 


can  "  take  off  "  from,  and  land  on,  any  large,  smooth  piece  of 
ground.  Seaplanes  (Fig.  161)  have  water-tight  boat-shaped 
bodies  which  enable  them  to  take  off  from,  and  land  on,  the 
water.  Usually  there  is  also  a  smaller  pontoon  or  float  under- 
neath each  tip  of  the  lower  wing  to  balance  the  plane  when  it 
is  not  flying. 

121.  What  supports  an  airplane.  A  balloon  rises  because  it 
and  its  gaseous  filling  weigh  a  little  less  than  the  air  displaced. 
An  airplane  is,  however,  much  heavier  than  the  air  it  displaces, 
and  is  kept  up  only  by  the  upward  pressure  of  the  air  against 
its,  wings. 

The  action  is  much  like  that  of  a  kite  floating  in  a  wind.  The 
moving  air  strikes  against  the  lower,  inclined  surface  of  the 

kite  and  is  deflected  downward, 
exerting  a  force  nearly  normal 
to  the  face  of  the  kite.  This 
force  and  the  pull  of  the  kite 
string  are  such  as  to  have  a 
resultant  pointing  straight  up, 
that  exactly  balances  the  weight 
of  the  kite. 

Direction  of  flight 

_,.,_,  In  the  case  of  the  airplane 

Fig.  160.    Forces  acting  on  an  airplane.  . 

there  is  also  a  rush  of  air  past 

the  wings,  although  it  is  due  to  the  motion  of  the  airplane  itself 
through  the  air,  rather  than  to  a  wind,  as  in  the  case  of  the 
kite.  This  rush  of  air  is  deflected  downward  and  gives  a 
thrust  OP,  as  shown  in  figure  160,  against  and  nearly  perpen- 
dicular to  the  wing  surface.  There  is  also  the  forward  thrust  OF 
of  the  propeller,  which  corresponds  in  a  way  to  the  pull  of 
the  kite  string.  Just  as  in  the  case  of  the  kite,  these  two  forces 
have  a  resultant  OR,  which  points  straight  up  and  balances 
the  weight  OW  of  the  airplane.  If  the  propeller  speed  increases, 
then  the  forward  thrust  OF  and  the  push  OP  of  the  air  against 
the  wings  increase.  Consequently  the  upward  resultant  force 
OR  is  greater  than  the  weight,  and  the  airplane  rises. 


SEAPLANES 


145 


146 


NON-PARALLEL  FORCES 


PROBLEMS 

1.   Figure  162  shows  a  simple  crane.     Find  the  tension  in  the  tie  rope 
EC  and  the  push  of  the  brace  AC,  when  the  weight  W  is  one  ton,  and 

the  angle  BAG  is  45°.      Neglect  the 
weight  of  the  brace. 

2.  In  figure  148  the  point  B  of  the 
canal  boat  is  10  feet  from  the  tow-path, 
and  a  pull  of  200  pounds  is  exerted  on 
the  50-foot  towline.     What  is  the  effec- 
tive component? 

3.  A  boy  weighing  120  pounds  sits 
of  a  simple    in  a  hammock  whose  ropes  make  angles 

of  30°  and  60°,  respectively,  with  the 
What  is  the  tension  in  each  rope  ? 


000  Ibs. 


vertical. 


4.  Each  rope  in  problem  3  is  fastened  to  a  hook  in  the  ceiling.     Find 
the  vertical  pull  on  each  hook. 

6.  One  end  of  a  horizontal  steel  girder  10  feet  long  rests  on  a  ledge 
in  the  wall,  and  the  other  end  is  supported  by  a  chain  arranged  as  shown 
in  figure  163.  Assuming  that  the  girder 
weighs  40  pounds  per  foot,  find  the  ten- 
sion in  the  chain. 

6.  If  the  point  where  the  chain  in 
problem  5  is  attached  to  the  wall  had 
been  only  5  feet  above  the  girder,  what 
would  the  tension  in  the  chain  have  been  ? 
Why  is  the  tension  in  this  position  so 
much  more  than  in  the  position  of  prob- 
lem 5? 


7.  The  net  lift  of  a  captive  balloon  is 
250  pounds,  and  it  is  held  by  an  anchor 
rope  which  makes  an  angle  of  60°  with 

the  ground.     Compute  the  tension  in  the  Fig.    163.       Girder    supported 
anchor  rope  (assumed  to  be  straight),  and  from  a  walL 

the  horizontal  force  exerted  by  the  wind  against  the  balloon. 

8.  A  child  weighing  60  pounds  is  sitting  in  a  swing,  the  seat  of  which 
is  12  feet  below  the  support,   (a)  What  horizontal  force  is  required  to 
hold  the  child  6  feet  to  the  left  of  the  vertical  line?   (6)  What  is  the 
tension  in  each  rope  ? 


SUMMARY  147 

SUMMARY  OF  PRINCIPLES  IN  CHAPTER  V 

Forces  can  be  represented  by  arrows  drawn  to  scale : 
Direction  indicated  by  the  arrowhead, 
Point  of  application  by  the  tail, 
Magnitude  of  force  by  the  length. 

The  parallelogram  of  forces : 

The  resultant  of  two  forces  is  the  diagonal  of  a  parallelogram 

constructed  on  arrows  representing  the  two  forces. 
The  equilibrant  of  two  forces  is  equal  and  opposite  to  their 
resultant. 

Resolution  of  forces : 

A  single  force  may  be  resolved  into  two  forces   acting   in 

given  directions,  by  constructing  a  parallelogram  whose 

diagonal   represents   the   given  force,  and  whose  sides 

have  the  given  directions. 
If  the  parallelogram  is  a  rectangle,  either  side  represents  the 

useful  component  of  the  force  in  that  direction. 

If  three  forces  act  on  a  body  in  equilibrium,  their  lines  of  action 
must  pass  through  a  single  point  or  be  parallel. 

QUESTIONS 

1.  Show  by  a  diagram  the  useful  component  of  the  pull  exerted  on 
a  sled  by  a  rope. 

2.  Why  is  a  long  towline  more  effective  in  hauling  a  canal  boat  than 
a  short  line  ? 

3.  Why  does  one  lower  the  handle  in  pushing  a  lawn  mower  through 
tall  grass? 

4.  A  boat  is  rowed  across  a  river,    (a)  What  two  forces  are  acting 
on  the  boat?     (6)  In  what  direction  should  one  row  in  order  to  land 
directly  opposite  ? 

6.  A  child  sitting  in  a  swing  is  gradually  drawn  aside  by  a  force 
which  continually  acts  in  a  horizontal  direction.  Does  the  tension  in 
the  swing  rope  grow  smaller  or  larger  ?  Explain. 


148 


NON-PARALLEL  FORCES 


6.  Why  will  a  long  rope,  hanging  between  two  points  at  the  same 
level,  break  before  it  can  be  pulled  tight  enough  to  be  straight  ? 

7.  Find  in  some  building  a  roof  truss  with  a  steel  tie  rod  to  keep 
it  from  spreading. 

8.  How  are  the  walls  of  Gothic  cathedrals  strengthened  so  that  they 

can  exert  the  side  thrust  necessary  to 
hold  up  the  roof  ? 

9.  Explain  why  the  toggle-joint  used 
to  expand  an  automobile  brake  (Fig. 
164)  has  such  a  large  mechanical  ad- 
vantage. Draw  isolation  and  force  dia- 
grams. Explain  how  the  principle  of  the 
toggle-joint  may  be  used  in  tightening 
the  sail  of  a  cat-boat. 

10.  Could  an  ordinary  balloon  "  tack  " 
against  the  wind  like  a  sailboat  if  it 
were  provided  with  a  sail,  a  large  keel, 
and  a  rudder,  like  a  sailboat?  Why? 


Fig.  164.     Toggle-joint  used  to 
expand  automobile  brake. 


PRACTICAL  EXERCISE 

Bridges.  Examine  the  steel  bridges  in  your  neighborhood  to  see  if 
they  are  "  girder  bridges  "  or  "  framed  bridges,"  and,  if  any  of  them  are 
framed,  see  whether  they  are  pinned  or  riveted,  and  which  members 
are  compression  members,  and  which  tension.  Make  a  sketch  like 
that  in  figure  156  of  one  of  these  bridges,  showing  the  compression 
members  by  heavy  lines.  If  possible,  make  a  model  bridge  of  wood 
and  wire.  Be  careful  about  loading  it  near  either  end.  Why? 


CHAPTER  VI 
ELASTICITY  AND   STRENGTH  OF  MATERIALS 

The  different  kinds  of  stress  —  stress  and  strain  —  Hooke's 
law  —  elastic  limit  —  breaking  strength  —  commercial  test- 
ing machines  —  factor  of  safety. 

122.  Importance  of  studying  materials.    A  structural  en- 
gineer who  is  to  build  a  bridge,  a  building,  or  a  machine  must 
know  not  only  the  forces  that  will  be  exerted  on  each  of  its 
parts,  but  also  the  strength  of  the  wood,  brick,  stone,  concrete, 
or  steel  of  which  they  are  to  be  made.   This  knowledge  can  be 
gained  only  by  testing  each  kind  of  material  with  the  greatest 
care.     For  this  reason,  every  engineering  handbook  tabulates 
the  results  of  a  great  number  of  tests  of  this  kind.     Every  large 
manufacturer  of  steel  girders  or  rails  maintains  a  testing  labo- 
ratory so  that  he  can  sell  his  products  under  a  strength  guar- 
antee.    Even  textile  manufacturers  test  the  breaking  strength 
of  the  yarn  that  goes  into  their  cloth.     Indeed,  the  study  of 
the  strength  of  materials  is  regarded  as  of  such  importance  to 
the  public  that  the  government  itself  maintains  a  bureau  for 
the  purpose.     In  this  chapter  we  shall  learn  how  such  tests 
are  made,  and  how  the  results  are  used. 

123.  The  different  kinds  of  stresses.     In  designing  a  beam 
or  column  or  some  part  of  a  machine,  an  engineer  must  first 
know  how  the  force  it  is  to  resist  will  be  applied. 

For  instance,  the  cable  that  supports  an  elevator,  or  the 
rope  of  a  swing,  or  a  belt  that  is  transmitting  power  from  one 
pulley  to  another  has  to  resist  a  pull  applied  at  each  end,  which 
tends  to  stretch  it,  and  may,  perhaps,  break  it  by  pulling  one 
part  of  it  away  from  the  next.  In  such  a  case  we  say  that  the 
"  member  "  -  that  is,  the  cable  or  rope  or  belt  —  is  in  ten- 
sion, meaning  "  in  a  state  of  tension." 

149 


150      ELASTICITY  AND  STRENGTH   OF   MATERIALS 


The  pier  of  a  bridge,  or  the  foundation  of  a  house,  or  a  post 
supporting  a  piazza  roof  has  to  do  something  quite  different 
from  this.  It  has  to  resist  a  push  at  each  end,  which  tends  to 
shorten  it,  and  may  cause  it  to  give  way  by  crushing  it.  In 
such  a  case  we  say  that  the  member  —  that  is,  the  pier  or 
foundation  or  post  —  is  in  compression,  meaning  "  in  a  state 
of  compression." 

A  floor  beam  in  a  house  or  a  girder  in  a  plate-girder  bridge 
is  subjected  to  a  transverse  stress  and  has  to  resist  bending. 
If  it  gives  way  at  all,  it  does  so  by  breaking  in  two  like  a  stick 
broken  across  one's  knee. 

The  duty  of  the  driving  shaft  that  connects  the  engine  with 
the  rear  wheels  of  an  automobile,  or  of  the  shafts  that  run 
overhead  in  many  factories  and  transmit  power  to  the  various 
machines,  is  to  resist  twisting. 

And,  finally,  the  duty  of  a  rivet  (Fig.  165)  in  a  steel  struc- 
ture is  different  from  any  of  these.  It  has  to  keep  one  of  the 

plates  from  sliding  over  the  other. 
When  such  a  rivet  gives  way,  it  is 
often  because  the  halves  of  it  have 
been  pushed  sidewise  so  hard  that 
one  has  slid  away  from  the  other, 
leaving  a  flat,  clean  break  parallel  to 
the  surface  separating  the  plates.  It 
is  a  stress  of  this  sort  that  we  put  on 
a  piece  of  cloth  or  paper  when  we  cut 
it  with  a  pair  of  shears.  So  we  say  that  the  rivet  is  in  shear, 
meaning  that  it  is  in  the  same  state  as  if  it  were  being  cut  in 
two  by  a  huge  pair  of  shears. 

There  are,  then,  these  five  kinds  of  stresses:  tension,  compres- 
sion, bending,  twisting,  and  shear.  In  each  case  that  material 
and  shape  should  be  used  which  will  best  resist  the  particular 
kind  of  stress  that  is  to  be  applied.  Thus  bricks  set  in  mortar 
do  very  well  under  compression,  but  are  of  little  use  in  resisting 
any  of  the  other  kinds  of  stress.  Steel  will  resist  any  of  them 


Fig.  165.     Shearing  action  of 
plates  on  rivet. 


RELATION  OF  STRAIN  TO  STRESS 


151 


well.     Cast  iron  will  resist  compression  about  four  times  as 
well  as  it  will  tension,  and  so  on. 

124.  Stress  and  strain.  Whenever  any  one  of  these  kinds 
of  stress  is  applied  to  a  body,  the  body  yields  a  little.  No 
bridge  girder  is  stiff  enough  not  to  bend  a  little  under 
every  truck  or  train  that  goes  over  the  bridge.  If  it 
is  a  good  girder,  the  amount  of  bending  is  imper- 
ceptible to  ordinary  observation ;  but  there  is  always 
some  bending.  Similarly,  every  driving  shaft  in  an 
automobile  twists  a  little  when  it  is  transmitting 
power.  The  same  can  be  said  of  the  other  types  of 
stress ;  each  of  them  always  causes  some  yielding  or 
deformation  of  the  body  under  stress. 

The  word  "  strain  "  is  used  in  mechanics  to  de- 
scribe the  deformation  produced.     The  word  stress 

always  refers  to  the 
forces  which  are  acting, 
while  the  word  strain 
refers  to  the  effect 
which  they  produce. 

125.  Relation  of 
strain  to  stress.  Let 
us  try  some  experi- 
ments to  see  if  there  is  any  relation  between  the  amount  of 
stress  applied  to  a  body  and  the  amount  of  strain  it  produces. 

I.  Tension.  Let  us  fasten  one  end  of  a  piece  of  steel  or  spring-brass 
wire  in  a  clamp  near  the  ceiling,  and  attach  a  pan  for  weights  to  the 
lower  end  of  the  wire  (Fig.  166).  Since  the  stretch  will  be  small,  it  is 
necessary  to  use  a  lever  or  some  other  device  to  magnify  it.  Having 
placed  just  enough  weight  in  the  pan  to  straighten  the  wire,  we  add 
weights  one  at  a  time  and  read  the  corresponding  positions  of  the 
pointer.  Each  time  we  must  remove  the  added  weights  to  see  if  the 
pointer  comes  back  to  its  original  position.  When  it  fails  to  do  this, 
we  stop  the  experiment  and  disregard,  for  the  moment,  the  last  read- 
ing of  the  pointer.  If  we  then  compute  from  each  deflection  of  the 
pointer  the  actual  stretch,  or  elongation,  of  the  wire,  and  divide  each 


Fig.   1 66.     Stretching  a  wire  with 
different  loads. 


152      ELASTICITY  AND  STRENGTH   OF   MATERIALS 


stretch  by  the  force  causing  it,  we  find  that  all  the  quotients  are  ap- 
proximately the  same.     That  is,  the  stretch  is  proportional  to  the  load. 

II.  Compression.   The  same  is  true  for  compression.     Thus  experi- 
ments show  that  under  ordinary  conditions  the  compression  of  a  spring 
is  proportional  to  the  force  applied. 

III.  Bending.   We  can  perform  a  similar  experiment  for  bending 
by  supporting  a  metal  rod  or  tube  on  knife  edges,  and  hanging  dif- 
ferent weights  from  the  center.     A  lever,  like  that  used  in  the  tension 

experiment  above,  or  a  micrometer 
screw  enables  us  to  measure  the 
small  deflections  of  the  center  of 
the  rod.  As  before,  we  find  that 
the  deflections  are  proportional  to  the 
loads  causing  them. 

IV.  Twisting.  The  apparatus 
shown  in  figure  167  enables  us  to 
perform  similar  experiments  on 
twisting.  The  metal  rod  is  clamped 
fast  at  the  right-hand  end  and  is 
clamped  at  the  left  in  the  hub  of 
the  wheel.  Weights  placed  in  the 
pan  exert  a  twisting  force  on  the  rod, 
and  the  amount  of  twist  produced 
can  be  read  off  on  the  rim  of  the 
wheel.  As  before,  we  find  that  the 
twist  is  proportional  to  the  stress  caus- 
ing it,  namely,  the  torque,  or  moment  of  the  twisting  force.  Thus,  one 
pound  acting  at  a  distance  (radius)  of  one  foot  exerts  a  torque  of  one 
pound  foot. 

In  all  these  cases,  the  strain  is  proportional  to  the  stress.  This 
is  called  Hooke's  law,  after  the  scientist  who  discovered  it. 
Hooke's  law  applies  to  all  kinds  of  strains,  if  the  stresses  are 
not  too  great. 

PROBLEMS 

1.  If  a  weight  of  1  pound  when  hung  on  a  certain  spring  lengthens 
it  2  inches,  what  weight  would  lengthen  it  -J  of  an  inch  ?     How  much 
would  f  of  a  pound  lengthen  it  ? 

2.  If  a  force  of  5  pounds  is  required  to  move  the  middle  point  of  a 
beam  ^  of  an  inch,  what  force  would  move  it  ^  of  an  inch  ? 


Fig.  167.    Apparatus  for  twisting  metal 
rods. 


ELASTIC  LIMIT  AND  BREAKING  STRENGTH       153 


3.  A  2-pound  force  is  applied  to  the  rim  of  a  wheel  9  inches  in  diam- 
eter in  the  torsion  apparatus  described  in  section  125,  and  the  end  of 
the  rod  twists  through  3°.     What  force  would  have  to  be  applied  to  the 
rim  of  a  wheel  12  inches  in  diameter  to  make  the  end  of  the  same  rod 
twist  through  5°  ? 

4.  An  experiment  to  find  the  relation  of  the  bending  of  a  beam 
to  the  load  gave  the  following  data : 


LOADS 
in  pounds 

10 

20 

30 

40 

50 

60 

70 

BENDING 
in  inches 

0.05 

0.10 

0.15 

0.21 

0.25 

0.29 

0.35 

Plot  these  values,  making  the  loads  vertical  and  the  bendings  hori- 
zontal.    What  law  is  here  illustrated? 

5.   A  piece  of  steel  piano  wire  90  inches  long  and  0.035  inches  in 
diameter  was  stretched  with  various  loads  as  follows : 


LOADS 
in  pounds 

5 

10 

15 

20 

25 

STRETCHING 
in  inches 

0.016 

0.033 

0.048 

0.064 

0.079 

Plot  a  curve  to  show  the  relation  of  the  stretching  to  the  load.     Make 
the  loads  ordinates  (vertical)  and  the  stretches  abscissas  (horizontal). 

126.  Elastic  limit  and  breaking  strength.  In  the  tension 
experiment  in  the  last  section  we  found  that  when  a  sufficiently 
great  load  was  hung  from  the  wire,  the  latter  did  not  come  back 
to  its  original  length  when  the  load  was  removed.  It  had 
acquired  a  permanent  "set."  The  same  thing  is  true  of  other 
kinds  of  stress,  and  would  be  noticed  in  the  other  experiments 
if  the  stresses  were  made  great  enough.  The  smallest  stress 
of  any  particular  kind  that  will  cause  a  permanent  set  in  a  body 
is  called  the  elastic  limit  of  the  body  for  that  particular  kind 
of  stress.  As  long  as  the  load  is  below  the  elastic  limit,  Hooke's 
law  holds;  but  stresses  greater  than  the  elastic  limit  cause 
deflections  greater  than  Hooke's  law  predicts. 


154      ELASTICITY   AND  STRENGTH   OF   MATERIALS 


If  we  still  further  increase  the  load  in  the  tension  experi- 
ment, we  finally  reach  a  load  so  great  that  the  wire  stretches 
very  rapidly  and  almost  immediately  breaks.  This  is  also 
true  of  other  kinds  of  tests,  such  as  tests  for  bending.  The 
smallest  stress  of  any  particular  kind  that  will  cause  a  body 
to  give  way  is  called  the  ultimate  or  breaking  strength  of  the 
body  for  that  particular  kind  of  stress. 

Usually  the  elastic  limit  of  anything  is  much  smaller  than 
its  breaking  strength.  But  certain  materials,  such  as  glass, 
follow  Hooke's  law  up  to  their  breaking  points,  and  never 
show  a  permanent  set. 

127.  Commercial  testing.  Tension,  compression,  and  trans- 
verse tests  on  specimens  of  steel  and  other  metals  are  made 

commercially  on  a  ma- 
chine like  that  shown 
in  figure  168. 

The  machine  consists 
essentially  of  three  parts : 
(1)  the  platform  balance, 
which  has  a  weighing 
table  C  and  three  levers 
so  constructed  as  to  act 
as  a  single  lever;  (2) 
the  stressing  mechanism, 
which  pulls  down  the 
movable  crosshead  B  by 
means  of  four  pulling 
screws  with  rotating  nuts 
inside  the  base  plate ; 
and  (3)  the  driving  mechanism,  which  turns  the  rotating  nuts  at  varying 
speeds  by  power  received  from  a  direct-connected  electric  motor.  For 
tension  tests,  the  specimen  is  fastened  to  the  stationary  crosshead  A 
and  to  the  movable  crosshead  B.  For  compression  tests  it  is  placed 
between  the  movable  crosshead  B  and  the  weighing  table  C.  For 
transverse  tests,  the  specimen  is  supported  on  two  V-blocks  placed  on 
the  weighing  table  C,  and  the  top  V-block  is  secured  to  the  movable 
crosshead  B  as  in  compression  tests.  In  all  these  tests  it  is  possible 
to  operate  the  machine  automatically. 


ctric 


Fig.  1 68.     Commercial  testing  machine. 


FACTOR  OF  SAFETY 


155 


Most  commercial  testing  machines  are  so  arranged  that  they 
can  draw  automatically  a  stress-strain  curve  for  the  material 
under  test.  A  paper-covered  drum  is  turned  by  a  multiply- 
ing mechanism  attached  to  the  ends  of  the  specimen  in  such  a 
way  that  the  rotation  of  the  drum  is  proportional  to  the  stretch 
or  contraction  of  the  specimen.  Meanwhile  a  pencil  is  moved 
up  and  down  along  the  drum  and  indicates  the  force  applied 
at  each  instant. 

Figure  169  is  an  example  of  such  a  diagram.  The  straight  portion 
OA  is  in  accordance  with  Hooke's  law.  The  elastic  limit  is  where  the 
curve  begins  to  bend.  It 
is  not  very  clearly  marked 
but  is  near  A.  At  B  occurs 
what  is  called  the  "drop 
of  the  beam."  The  speci- 
men undergoes  some  curi- 
ous and  rather  sudden 
internal  rearrangement  of 
molecules  and  stretches  so 
fast  for  an  instant  that 
the  machine  cannot  keep 
up.  This  accounts  for  the 
temporary  drop  in  the  force 

Between  C  and  D  the  specimen  stretches 


Elongation 


Fig.  169.     Stress-strain  curve. 


exerted  by  the  machine. 

more  and  more  rapidly,  and  final  rupture  begins  to  occur  at  D. 

The  interesting  quantities  determined  by  such  a  test  are  (1)  the 
stress  at  B,  which  is  commonly  used  instead  of  the  rather  vaguely 
defined  elastic  limit  A,  (2)  the  stress  at  D,  which  is  the  ultimate 
strength  of  the  specimen,  and  (3)  the  elongation  OP  at  rupture.  The 
latter  is  a  useful  indication  of  toughness  or  lack  of  brittleness. 

128.  Factor  of  safety.  An  engineer,  when  designing  a  bridge 
or  a  machine,  must  be  absolutely  sure  that  no  part  of  it 
will  ever  be  subjected  to  a  stress  greater  than  its  elastic 
limit ;  for  if  this  were  to  happen,  that  part  would  be  perma- 
nently deformed,  and  this  would  weaken  the  rest  of  the  struc- 
ture, or  at  least  throw  it  out  of  alignment.  He  therefore  plans 
to  make  each  member  strong  enough  to  carry  several  times 
as  much  load  as  will  probably  ever  be  imposed  on  it.  This  is 


156      ELASTICITY  AND  STRENGTH  OF  MATERIALS 

partly  to  provide  for  any  unforeseen  temporary  overloading 
of  the  structure,  and  partly  because  there  may  be,  even  in 
materials  of  the  best  quality,  imperceptible  flaws  that  would 
make  the  completed  member  less  strong  than  it  seems  to  be. 
The  number  of  times  that  the  load  planned  for  is  greater  than  the 
load  expected  is  called  the  factor  of  safety. 

The  factor  that  should  be  used  varies  with  the  material ; 
thus  it  is  commonly  10  for  brick  and  stone,  and  only  4  for  steel. 
It  also  varies  with  the  nature  of  the  load ;  thus  it  is  commonly 
larger  when  the  load  is  to  be  intermittent,  as  in  machines  or 
railroad  bridges,  than  when  it  is  to  be  steady,  as  in  buildings. 
Often  the  factor  for  buildings  is  taken  larger  than  would  other- 
wise be  necessary,  so  that  there  may  be  no  danger  of  deflec- 
tions in  the  walls  and  ceilings  great  enough  to  crack  the  plaster. 

SUMMARY  OF  PRINCIPLES  IN   CHAPTER  VI 

Stress  refers  to  force  acting. 

Strain  refers  to  deformation  produced. 

Hooke's  law :  Strain  is  proportional  to  stress. 

True  for  all  kinds  of  stress,  such  as  tension,  compression, 
bending,  and  twisting. 

Elastic  limit  is  the  minimum  stress  that  will  produce  a  perma- 
nent set.  Hooke's  law  applies  only  for  loads  below  the 
elastic  limit. 

Breaking  strength  is  the  minimum  stress  that  will  cause  a 
body  to  give  way. 

elastic  limit 

Factor  of  safety  =  : — — -    — -  - 

permissible  load 

QUESTIONS 

1.  Name  five  practical   applications    of   the   elasticity  of  steel  in 
springs. 

2.  Arrange  an  apparatus  to  determine  whether  or  not  Hooke's  law 
applies  to  a  rubber  band.  - 


PRACTICAL  EXERCISES 


157 


3.  Name  the  kinds  of  stresses  which  are  acting  on  the  following: 
wires  of  a  piano,  crank  shaft  in  an  engine,   smokestack,   table  leg, 
belt,  pump  piston,  and  threads  holding  buttons  on  a  coat. 

4.  In  the  loading  of  long  thin  columns,  what  other  effects  besides 
simple  compression  have  to  be  considered  ? 

5.  Where  is  the  elastic  medium  in  the  human  body  which  prevents 
injury  to  the  brain  when  we  jump  ? 

6.  Try  to  find  out  what  is  meant  by  the  "fatigue"  of  metals  (see 
an  encyclopedia). 

7.  What  advantages  has  reenf  orced  concrete  over  ordinary  concrete 
for  building  purposes  ? 

8.  How  are  the  walls  of  high  office  buildings  supported,  and  why  ? 

PRACTICAL  EXERCISES 

1.   Automatic    door-closer.     Figure   170  shows  how  one  of  these 
devices  is  attached  to  a  door  and  how  it  is  built.     Get  one  of  these 


Fig.  170.     Automatic  door-closing  spring. 

attachments  from  a  hardware  dealer  and  find  out  just  how  it  works. 
How  is  the  banging  of  the  door  prevented  in  this  device? 

2.  Shock  absorber.  What  is  the  purpose  of  a  shock  absorber 
on  an  automobile?  Find  out  how  some  form  of  absorber  works. 
What  principles  are  applied  ? 


CHAPTER  VII 
ACCELERATED   MOTION 

Speed  and  acceleration  —  laws  of  motion  at  constant  accel- 
eration —  falling  is  motion  at  constant  acceleration  —  value 
of  acceleration  of  gravity  —  projectiles. 

129.  Average  speed.  If  a  man  walks  12  miles  in  3  hours, 
we  say  that  he  averages  4  miles  an  hour.  To  be  sure,  at  any 
particular  point  on  his  journey  he  may  have  been  going  faster 
or  slower ;  but  his  average  speed  or  velocity  is  4  miles  an  hour. 
If  we  know  that  the  average  speed  of  a  steamer  is  22  miles  an 
hour,  we  can  find  a  day's  run  by  multiplying  the  average  speed 
by  the  number  of  hours  in  a  day  ;  thus,  22  X  24  =  528  miles. 
In  general, 

Distance  =  average  speed  X  time. 

Speed  is  expressed  in  various  ways  ;  for  example,  we  say  that 
an  automobile  is  traveling  at  the  rate  of  25  miles  an  hour, 
that  a  steamer  is  doing  18  knots,  or  18  nautical  miles  an  hour, 
and  that  a  rifle  ball  goes  2000  feet  per  second.  Engineers  and 
other  scientific  men  commonly  express  speeds  in  miles  per 
hour  (mi./hr.),  feet  per  second  (ft./sec.),  or  centimeters  (or 
meters)  per  second  (cm. /sec.  or  m./sec.).  The  following  table 
gives  some  typical  speeds  : 

TABLE  OF  SPEEDS 

Soldiers  marching         3     mi./hr.      =       4.4  ft./sec.  =     1.3  m./sec. 

Athlete  (mile  run)       14     mi./hr.      =     20.5  ft./sec.  =     6.3  m./sec. 

Athlete  (100  yds.)       20.4  mi./hr.      =     30     ft./sec.  =     9.1  m./sec. 

Ocean  steamer  27     mi./hr.      =     39.6  ft./sec.  =   12.1  m./sec. 

Express  train  50     mi./hr.      =     73.5  ft./sec.  =  22.4  m./sec. 

Wind  in  hurricane     110     mi./hr.      =   162     ft./sec.  =  49     m./sec. 

Airplane  194     mi./hr.      =  285     ft./sec.  =  87     m./sec. 

Sound  750     mi./hr.      =1100     ft./sec.  =335     m./sec. 

Rifle  ball  1360     mi./hr.      =2000     ft./sec.  =610     m./sec. 

158 


VARIABLE  SPEED  159 

PROBLEMS 

(In  solving  these  problems  use  data  given  in  table  of  speeds  when  necessary.) 

1.  Sixty  miles  an  hour  equals  how  many  feet  per  second?     (You 
would  do  well  to  remember  this  number.) 

2.  If  the  distance    across  the  Atlantic  Ocean  is  3000  miles,  how 
many  days  will  it  take  a  steamer  to  cross? 

3.  How  long  will  it  take  an  express  train  to  cover  40  miles  ? 

4.  In  what  time  (minutes  and  seconds)  can  the  athlete  referred  to 
in  the  table  do  the  mile  run? 

5.  The -time  for  a  4-mile  boat  race  was  21  minutes  and  10  seconds, 
(a)    What  was  the  average  speed  in  feet  per  second?     (6)    In  miles 
per  hour? 

6.  If  an  automobile  wheel  is  32  inches  in  diameter  and   the  car 
is  moving  at  the  rate  of  20  miles  an  hour,  how  many  revolutions  per 
minute  (r.  p.  m.)  does  the  wheel  make? 

7.  An  automobile  is  going  30  miles  an  hour.     A  motor  cycle  is  5 
miles  behind  it  and  going  40  miles  an  hour.     How  long  will  it  take 
the  motor  cycle  to  overtake  the  automobile? 

8.  A  rifle  is  fired  at  a  target  half  a  mile  away.      How  long  after  it 
is  fired  does  the  sound  it  makes  against  the  target  reach  the  man  with 
the  rifle? 

130.  Variable  speed.  When  a  train  is  starting  out  from 
a  station,  it  is  gaining  speed,  and  when  it  is  approaching  a 
station  where  it  must  stop,  it  is  losing  speed.  So  we  see  that, 
on  account  of  stops  and  differences  in  grade,  the  speed  of  a 
train  is  not  uniform  or  constant,  but  is  changing  or  variable. 
A  loaded  sled  which  starts  at  the  top  of  a  long  hill  gains  in 
speed  as  it  descends  the  hill;  but  when  it  reaches  the  level 
ground  at  the  bottom,  it  is  retarded  and  loses  speed  until  it 
stops.  Its  speed  or  velocity,  starting  at  zero,  has  increased 
to  a  maximum  and  then  has  decreased  to  zero  again.  Similarly, 
the  speed  of  a  projectile  from  a  big  gun  or  of  the  piston  of  an 
engine  is  not  uniform  but  variable. 

Formerly,  when  a  policeman  wished  to  determine  the  speed 
of  an  automobile  at  any  point,  he  measured  off  some  convenient 


160 


ACCELERATED  MOTION 


distance  near  the  point  and  then  got  the  time  which  elapsed 
while  the  automobile  traveled  the  fixed  distance.  For  ex- 
ample, if  the  measured  distance,  sometimes  called  a  "  trap," 
was  a  quarter  of  a  mile  and  the  time  was  20  seconds,  the  speed 
was  three  quarters  of  a  mile  per  minute,  or  45  miles  per  hour. 
But  if  the  driver  of  the  automobile  was  aware  of  the  trap  and 
was  driving  at  a  dangerously  high  speed  at  the  beginning  of 
the  trap,  he  would  slow  down  so  that  his  average  speed  over 
the  measured  distance  would  be  within  the  limit.  To  catch 
such  a  driver,  that  is,  to  get  his  speed  more  accurately  at  any 
point,  one  took  as  short  a  distance  as  was  consistent  with  an 
accurate  measurement  of  the  time. 

131.  The  speedometer.  Nowadays  a  traffic  policeman  trails 
a  speeding  automobilist  on  a  motor  cj^cle,  and  determines  the 
speed  at  any  given  instant  by  reading  his  own  speedometer. 

The  essential  parts  of  a  speedometer  of  the  centrifugal  type  are 

shown  in  figure  171.  A  shaft  A  A  runs  in  ball  bearings  and  is  driven 

through  a  flexible  shaft  by  a  gear  at- 
tached to  one  of  the  wheels,  or  to  the 
main  driving  shaft.  The  faster  the  car 
goes,  the  faster  the  shaft  A  A  rotates. 
Two  or  three  weights  BB  are  carried 
by  links  hinged  at  C  to  the  shaft  and 
at  D  to  a  collar  that  can  slide  up  and 
down  the  shaft.  The  faster  the  shaft 
rotates,  the  more  the  weights  BB  tend 
to  fly  out.  This  tendency  is  balanced 
by  the  spring  which  pushes  down  on 
the  collar  D.  At  any  given  speed  the 
collar  D  rises  just  so  much  against  the 
increasing  push  of  the  spring,  and  moves 
the  pointer  F  by  means  of  the  bell  crank 
and  geared  sector.  The  light  spring  H 

Fig.  171.  Diagram  of  the  essential  serves  to  keep  the  little  roller  pressing 
parts  of  an  automobile  speed-  against  the  collar  D.  A  speedometer 

also  measures  distance  by  making  the 

revolutions  of  the  shaft  A  A  drive  a  counting  device  K  through  a 

double  worm-gear  speed  reduction  MN. 


ACCELERATION  161 

,  132.  Acceleration.  It  is  unpleasant  to  be  on  a  street  car 
when  it  starts  or  stops  too  suddenly.  This  suggests  the  prob- 
lem of  measuring  a  rate  of  change  of  speed,  which  is  called 
acceleration.  It  has  been  found  that  a  city  street  car  standing 
at  rest  can  safely  gain  speed  so  that  at  the  end  of  10  seconds 
it  is  going  15  miles  per  hour.  Assuming  that  this  gain  in 
speed  is  made  at  a  constant  rate  (only  constant  accelerations 
will  be  discussed  in  this  book),  the  speed  of  the  car  increased 
1.5  miles-per-hour  every  second.  In  other  words,  the  accel- 
eration was  1.5  miles-per-hour  per  second.  Or,  since  15  miles 
an  hour  is  22  feet  per  second,  we  can  say  that  the  gain  in  speed 
each  second  is  2.2  feet  per  second. 
In  general, 

Acceleration  =  change  in  speed  per  unit  time, 
and  acceleration  is  always  to  be  expressed  as  so  many  speed 
units  per  time  unit.  Since  there  are  many  different  speed 
units,  such  as  miles-per-hour,  kilometers-per-hour,  feet-per- 
second,  and  centime ters-per-second,  there  are  many  ways  of 
expressing  the  same  acceleration.  Thus  the  acceleration  of 
the  electric  car  just  mentioned  is 

VELOCITY  UNIT  TIME  UNIT 

1.5  miles-per-hour  per  second, 

or    2.4  kilometers-per-hour        per  second, 

or    2.2  feet-per-second  per  second, 

or  67.0  centimeters-per-second  per  second. 

All  these  statements  mean  exactly  the  same  thing.  Engi- 
neers sometimes  use  the  first  two  expressions  for  acceleration; 
other  scientific  men  more  commonly  use  the  last  two.  It  is 
convenient  to  abbreviate  "  feet-per-second  per  second "  as 
ft./sec.2  and  "  centimeters-per-second  per  second  "  as  cm./sec.2 ; 
but  each  of  these  abbreviated  expressions  means  simply  so 
many  velocity  units  gained  per  second. 

The  accelerating  rates  of  cars  vary  according  to  service  and 
equipment,  but  the  following  rates  are  common  in  practical 
operation : 


162  ACCELERATED   MOTION 

TABLE  OF  ACCELERATIONS 

Steam  locomotive,  freight  service,  0.1-0.2  miles-per-hr.  per  sec. 
Steam  locomotive,  passenger  service,  0.2-0.5  miles-per-hr.  per  sec. 
Electric  locomotive,  passenger  service,  0.3-0.6  miles-per-hr.  per  sec. 
Electric  car,  interurban  service,  0.8-1.3  miles-per-hr.  per  sec. 

Electric  car,  city  service,  1.5         miles-per-hr.  per  sec. 

Electric  car,  rapid  transit  service,  1.5-2.0  miles-per-hr.  per  sec. 

133.  Positive  and  negative  acceleration.     When  the  speed 
is  increasing,  the  acceleration  is  said  to  be  positive,  and  when 
the  speed  is  decreasing,  the  acceleration  is  negative.     Thus, 
when  a  baseball  is  dropped  from  a  tower,  it  goes  faster  and 
faster;     it   has    positive    acceleration.     When,    however,    it    is 
thrown  upward,  it  goes  more  and  more  slowly;    it  has  nega- 
tive acceleration,  or  retardation. 

134.  Relation  of  speed  to  time  at  constant  acceleration. 
If  we  know  the  acceleration  of  any  body,  we  can  easily  com- 
pute its  speedjit  any  time  after  itjrtarted. 

FOR  EXAMPLE,  if  the  rate  of  acceleration  of  a  train  is  0.2  miles-per- 
houii_peiLseconjd,  how  fast  is  it  moving  one  minute  after  it  starts? 
One  minute  equals  60  seconds.  If  the  train  gains  0.2  miles-per-hour 
every  second,  then  its  speed,  60  seconds  after  starting,  would  be  60 
times  0.2,  or  12  miles  per  hour. 

LAW  I.  //  the  acceleration  is  constant,  the  speed  acquired  is 
directly  proportional  to  the  time. 

If  a  body  starts  from  rest,  we  have 

Final  velocity  =  acceleration  X  time 

\  v  =  at.  (I) 

PROBLEMS 

^1.    If  the  speed  of  an  electric  car  increases  every  second  2  feet  per 
second,  in  how  many  seconds  will  its  velocity  be  25  feet  per  second? 

2.  A  train  in  leaving  a  station  gains  speed  at  the  rate  of  0.5  miles- 
per-hour  per  second.     What  will  be  its  speed  (miles  per  hour)  at  the 
end  of  half  a  minute? 

3.  Express  1  mile-per-hour  per  second  in  feet-per-second  per  sec- 
ond. 


RELATION  OF  DISTANCE   TO   TIME  163 

4.  A  body  has  a  speed  of  16  feet  per  second  at  a  certain  instant,  and 
3  seconds  later  it  has  a  speed  of  112  feet  per  second.  What  is  its 
acceleration  ? 

A     5.    A  train  starting  from  rest  has,  after  33  seconds,  a  speed  of  15 
miles  an  hour.     What  is  the  average  acceleration, 

(a)  In  miles-per-hour  per  second? 

(b)  In  f  eet-per-second  per  second  ? 

.;*  X/P  y  3j 

6.  If  a  locomotive  can  give  a  train  an  acceleration  of  5  feet-per-sec- 
ond  per  second,  how  long  will  it  take,  after  slowing  down  for  a  cross- 
ing, to  increase  the  speed  of  the  train  from  22  feet  per  second  to  82  feet 
per  second?  -^'V^-^cat  ~  <*ojtp* 

7.  An  automobile  was  going  at  the  rate  of  30  miles  an  hour.     The 
brakes  were  applied  and  it  was^s  topped  in  10  seconds.     What  was  the 
rate  of  retardation  expressed  (a)  in  miles-per-hour  per  second,  and 
(6)  in  feet-per-second  per  second? 

A  8.  The  negative  acceleration  (retardation)  in  stopping  electric 
trains  is  seldom  greater  than  4  feet-per-second  per  second.  How  long 

does  it  take  to  stop  such  a  train  running  60  miles  an  hour?r  6°  x  £*'!-&*• 

• 

9.  What  is  the  acceleration  of  a  train  if  the  initial  speed  is  45  feet 
per  second,  and  after  5  seconds  the  speed  is  15  feet  per  second? 

10.  What  acceleration  (feet-per-second  per  second)  is  needed  in 
order  that  an  airplane  may  get  up  a  speed  of  60  miles  an  hour  in  half 
a  minute? 

135.  Relation  of  distance  to  time  at  constant  acceleration. 

Suppose  a  sled  gains  speed  at  a  constant  rate  as  it  goes  down 
a  hill.  If  its  acceleration  is  3  feet-per-second  per  second,  how 
far  will  it  go  in  the  first  five  seconds  after  starting  from  rest? 
We  have  already  seen  that  its  velocity  at  the  end  of  five  sec- 
onds will  be  5X3,  or  15  feet  per  second.  Now,  it  started 
from  rest,  that  is,  its  initial  velocity  was  zero,  and  gradually 
its  speed  increased  until  its  final  velocity,  at  the  end  of  five  sec- 
onds, is  15  feet  per  second.  Therefore  its  average  velocity  is 
one  half  the  sum  of  its  initial  and  final  velocities,  or  7.5  feet 
per  second. 

initial  velocity  -+-  final  velocity 


Average  velocity  = 


V 


2 

i/vA  4r 


164  ACCELERATED   MOTION 

We  have  already  learned   (section   129)   that  the  distance 
traversed  is  the  product  of  the  average  velocity  and  the  time. 

So  in  this  case  the  sled  has  gone  7.5  X  5,  or  37.5  feet. 
^  In  general,  for  a  body  starting  from  rest,  the  average  veloc- 
ity is  one  half  the  final  velocity : 

Average  velocity  =  \  v. 
But  we  already  know  that  the  final  velocity  is  v  =  at ;  then, 

Average  velocity  =  J  at.  ^i^ 
Therefore  the  distance  is 


/ 


*  =  \afi.  (II) 


LAW  II.  //  the  acceleration  is  constant,  the  distance  traversed 
from  rest  varies  as  the  square  of  the  time. 

In  using  this  law,  acceleration  should  be  expressed  in  ft.  /sec.2 
or  m./sec.2  or  cm.  /sec.2,  and  t  in  seconds. 

136.  Relation  of  speed  to  distance  at  constant  acceleration. 
Suppose  we  wished  to  know  how  far  the  rapid  transit  electric 
car  mentioned  in  the  table  in  section  132  would  have  to  run 
to  develop  a  speed  of  30  miles  an  hour,  starting  from  rest. 
Since  the  question  is  concerned  only  with  speed,  distance,  and 
acceleration,  it  is  convenient  to  have  an  equation  involving 
only  v,  ^  and  a. 

From  equation  (I)  we  have 

-•       &% 

and  from  equation  (II), 


Then,  y2  =  2a#                                           (HI) 

LAW  III.     //  a  body  starts  from  rest  and  the  acceleration  is 

constant,  the  speed  varies  as  the  square  root  of  the  distance  tra- 
versed. 


NEGATIVE  ACCELERATION  165 

Equation  (III)  enables  us  to  answer  the  question  about  the  electric 
car. 

v  =  30  miles  per  hour  =  44  feet  per  second 
a  =  2.2  feet-per-second  per  second 


Notice  that  30  miles  per  hour  and  2.2  feet-per-second  per  second 
could  not  be  substituted  directly,  because  two  different  kinds  of  time 
units,  namely,  hours  and  seconds,  and  two  different  kinds  of  distance 
units,  namely,  miles  and  feet,  are  involved. 

In  general,  all  the  quantities  substituted  in  any  equation 
must  first  be  expressed  in  consistent  units. 

Remember  that  laws  II  and  III  hold  only  for  bodies  starting 
from  rest.  It  will  save  time  to  memorize  equations  (I),  (II), 
and  (III).  Notice  that  there  is  an  equation  for  each  pair  of 
quantities  v  and  t,  s  and  t,  and  v  and  s.  Always  use  the  equa- 
tion that  gives  what  is  wanted  directly  -from  the  data. 

137.  Negative  acceleration.  Suppose  that  an  engineer,  run- 
ning at  50  miles  an  hour,  sees  a  child  on  the  track  200  yards 
ahead.  If  his  emergency  air  brakes  can  give  him  a  retardation 
of  4  feet-per-second  per  second,  can  he  stop  in  time? 

Here  we  have  a  problem  in  retardation,  or  negative  accelera- 
tion. Let  us  think  of  the  problem  the  other  way  around. 
Evidently  if  the  engineer  could  stop  within  a  given  distance  at 
a  given  retardation,  he  could  get  up  speed  within  the  same 
distance  with  an  equally  great  acceleration.  So  we  may  ask 
instead  whether  the  engineer  could  get  up  to  a  speed  of  50 
miles  an  hour  within  200  yards,  if  accelerating  at  4  feet-per- 
second  per  second.  The  answers  to  the  two  questions  are  the 
same. 

Since  the  quantities  involved  are  a  velocity  v  and  a  distance  s,  we 
use  equation  (III). 

y=50  miles  an  hour  =  73.3  ft.  /sec. 
a=4ft./sec.2 

Then  s  =  ^  =  (^^  =  672  feet  =224  yards. 

So  the  engineer  can  not  stop  in  time. 


166  ACCELERATED  MOTION 

PROBLEMS 

(Assume  constant  acceleration.) 

1.  If  a  locomotive  can  give  its  train  an  acceleration  of  0.6  feet-per- 
second  per  second,  in  what  distance  can  it  develop  a  speed  of  60  feet 
per  second,  starting  from  rest  ? 

2.  A  boy  runs  toward  an  icy  place  in  the  sidewalk  at  a  speed  of  20 
feet  per  second  and  slides  on  it  16  feet.     What  is  the  (negative)  accel- 
eration ? 

3.  How  far  wiH  a  marble  travel  down  an  inclined  plane  in  3  sec- 
onds if  the  acceleration  is  50  centimeters-per-second  per  second  ? 

A  motor  cycle  starting  from  rest  acquires  a  velocity  of  45  miles 
an  hour  in  1.5  minutes.  What  is  the  acceleration  in  miles-per-hour 
per  second? 

5.  How  many  yards  does  the  motor  cycle  go  in  problem  4  ? 

6.  In   an   advertisement   for   a  certain  brake   lining   it   is   stated 
that  (a)  an  automobile  moving  15  miles  an  hour  can  stop  in  20.8  feet ; 
and  (6)  if  moving  30  miles  an  hour  it  can  stop  in  83.3  feet.     Compute 
the  acceleration  (ft. /sec.2)  in  each  case. 

7.  If  the  acceleration  of  an  automobile   is   3  feet-per-second   per 
second,  what  speed  will  it  acquire  in  going  100  yards,  starting  from 
rest? 

18.  An  automobile  is  moving  at  the  rate  of  10  miles  an  hour,  when 
he  driver  presses  the  accelerator,  thus  giving  the  car  an  acceleration 
of  3  feet-per-second  per  second.  How  many  miles  an  hour  will  the 
car  be  moving  at  the  end  of  5  seconds  ?  V,  -  fLt~3'}t; 

138.  Falling  is  motion  at  constant  acceleration.  It  is  pos- 
sible to  determine  in  the  laboratory  the  time  it  takes  a  body 
to  fall  various  distances.  The  results  of  an  actual  series  of 
such  experiments  are  as  follows : 

DISTANCES  TIMES  RATIO  OF  TIMES 

36  cm.  0.272  sec.  3 

64  0.363  4 

100  0.452  5 

144  0.542  6 

It  will  be  seen  that  these  distances  vary  almost  exactly  as 
the  squares  of  the  times.  Thus,  36  is  to  64  as  32  is  to  42.  This 


t 


FALLING  BODIES  167 

we  have  just  seen  to  be  the  case  when  the  acceleration  is  con- 
stant (see  law  II).  Therefore  falling  is  a  case  of  motion  at  con- 
stant acceleration. 

A  freely  falling  body  acquires  velocity  so  rapidly  that  it  is 
difficult  to  make  observations  upon  it  directly.  Long  ago 
Galileo  hit  upon  the  plan  of  studying  the  laws  of  falling  bodies 
by  letting  a  ball  roll  down  an  incline.  In  this  way  he  "  di- 
luted "  the  force  of  gravity  and  increased  the  time  of  fall  so 
that  it  could  be  measured  more  accurately. 

139.  Galileo's  experiment  on  the  inclined  plane.    Galileo 
cut  a  trough  one  inch  wide  in  a  board  12  yards  long,  and  rolled 
a  brass  ball  down  the  trough.     After  about  one  hundred  trials 
made  for  different  inclinations  and  distances,   he   concluded 
that  the  distance  of  descent  for  a  given  inclination  varied  very 
nearly  as  the  square  of  the  time.    It  is  remarkable  that  he  was  so 
successful  in  this  experiment  when  we  consider  how  he  measured 
the  time.     He  attached  a  very  small  spout  to  the  bottom  of  a 
water  pail  and  caught  in  a  cup  the  water  that  escaped  during 
the  time  the  ball  rolled  down  a  given  distance.     Then  the 
water  was  weighed  and  the  times  of  descent  were  taken  as 
proportional  to  the  ascertained  weight. 

These  experiments  of  Galileo  are  especially  interesting  be- 
cause they  led  him  to  change  his  theories  about  the  distance 
and  time  of  falling  bodies.  He  seems  to  have  been  one  of  the 
first  of  the  early  philosophers  who  thought  it  necessary  to 
test  his  theories  by  experiment. 

140.  All  freely  falling  bodies  have  the  same  acceleration. 
In  1590,  people  still  believed  that  heavy  objects  fell  faster  than 
light  objects ;   in  other  words,  that  the  speed  of  a  falling  body 
depended  upon  its  weight.      But  Galileo  maintained  that  all 
bodies,  if  unimpeded  by  the  air,  fell  the  same  distance  in  the 
same  time,  and  that  the  only  thing  that  caused  some  objects, 
like  pieces  of  paper  or  feathers,  to  fall  more  slowly  than  pieces 
of  metal  or  coins  was  the  resistance  of  the  air.     To  convince 
his  doubting  friends  and  associates  he  caused  balls  of  different 


168 


ACCELERATED   MOTION 


sizes  and  materials  to  be  dropped  at  the  same  instant  from  the 
top  of  the  leaning  tower  of  Pisa.  They  saw  the  balls  start 
together,  and  fall  together,  and  heard  them 
strike  the  ground  together.  Some  were  con- 
vinced, others  returned  to  their  rooms  to  con- 
sult the  books  of  the  old  Greek  philosopher, 
Aristotle,  distrusting  the  evidence  of  their 
senses. 

Later,  when  the  vacuum  pump  was  invented, 
the  truth  of  Galileo's  view  was  confirmed  by 
dropping  a  feather  and  a  coin  in  a  vacuum  tube. 

If  we  place  a  piece  of  metal  and  some  light  object, 
like  a  bit  of  paper  or  pith  or  a  feather,  in  a  long 
tube  (Fig.  172)  and  pump  out  the  air,  we  find  that 
when  we  suddenly  invert  the  tube,  the  two  objects 
fall  side  by  side  from  the  top  to  the  bottom.  .If 
we  open  the  stopcock,  letting  the  air  in  again,  and 
repeat  the  experiment,  we  find  that  the  metal  falls 
to  the  bottom  first. 


and  coin  fall  to- 
gether  in  a  vac- 

uum. 


141.  Value  of  acceleration  of  gravity.  It  is 
to  determine  the  value  of  the  accelera- 
tion  of  gravity  from  the  experimental  data 
obtained  in  measuring  the  time  of  a  free  fall  (section  138)  ; 
it  is  also  possible  to  compute  the  value  of  this  constant  from 
the  data  got  in  the  experiment  of  rolling  a  ball  down  an  incline. 
Neither  of  these  methods,  however,  yields  as  precise  results 
as  are  obtained  in  experiments  with  pendulums. 

We  are  all  familiar  with  the  pendulum  as  a  means  used  to 
regulate  the  motion  of  clocks.  It  was  long  ago  discovered  by 
Galileo  that  the  successive  small  vibrations  of  a  pendulum  are 
made  in  equal  times  ;  and  that  the  time  of  vibration  does  not 
depend  on  the  weight  or  nature  of  the  bob,  or  the  length  of  the  swing, 
but  does  vary  directly  as  the  square  root  of  the  length  of  the  pen- 
dulum, and  inversely  as  the  acceleration  of  gravity.  This  is  ex- 
pressed in  the  following  formula  : 


fit 


ACCELERATION  OF  GRAVITY 


t  = 


16 


where  t  is  the  time  in  seconds  of  a  single  vibration,  I  is  the 
length  of  the  pendulum  in  centimeters,  g  is  the  acceleration  of 
gravity  in  centimeters-per-second  per  second,  and  TT  is  3. 14. 
We  can  measure  t  and  I  directly  and  TT  is 

Velocities        Distances 

known,  so  we  may  compute  g  from  the  for-  inft./8ec.     in/*. 
mula;  thus,  °  TI° 

(16.1) 
=   7TJ.  52.2J   B16.1 

P 

The  value  of  the  acceleration  of  gravity  is 
about  980  centimeters-per-second  per  second,  or 
about  32  2  feet-per-second  per  second.  It  varies 
a  little  from  place  to  place. 

Problems  about  falling  bodies  are  just  like 
other  problems  dealing  with  constant  accel- 
eration. In  the  equations  we  usually  repre- 
sent the  acceleration  of  gravity  by  g. 

Thus,  for  bodies  falling  freely  from  rest, 

v  =  gt, 


v2  =  2  gs. 


128.8 


(4S.3) 
C64.4 


(80.5) 


D1U.9 


(1H.7) 


ES57.6 


Fig.  173-     A  freely 
falling  ball. 


In  figure  173  we  have  plotted  the  distances  in 
feet  covered  by  a  freely  falling  body  in  successive 
seconds  and  also  the  velocities  in  feet  per  second 
acquired  at  the  end  of  each  second.  It  will  be 
seen  that  the  distance  covered  in  the  first  second 
AB  is  16.1  feet,  in  the  second  second  BC  48.3  feet, 
in  the  third  second  CD  80.5  feet,  etc.  These 
successive  distances  vary  as  the  odd  numbers  1,  3,  5,  7,  9,  etc. 

It  will  be  useful  to  remember  that  the  speed  with  which  a 
body  must  be  projected  upward  to  rise  to  a  given  height  is 
the  same  as  the  velocity  which  it  will  acquire  in  falling  from 
the  same  height.  (Compare  this  statement  with  section  137.) 


170 


ACCELERATED  MOTION 


PROBLEMS 

(Neglect  air  resistance  and  assume  g  =  32  ft. /sec.2,  or  980  cm. /sec.2.) 

1.   Make  a  table  like  the  following,  running  up  to  t=5  seconds, 
and  fill  it  in. 


NUMBER  OF 
SECONDS,  t 

TOTAL   DISTANCE 
FALLEN,  s  (FT.) 

SPEED  AT  END 
OF  EACH  SECOND, 
v  (FT.  /SEC.) 

TOTAL  DISTANCE 
FALLEN, 
s  (METERS) 

SPEED  AT  END 
OF  EACH  SECOND, 
0  (M./SEC.) 

1 
2 

16 

32 

--.r,-,,,. 

4.9 

9.8 

2.  A  stone  isj^oji^d  from  tce^tbp  of  a  cliff  and  strikes  at  the 
base  in  5   seconds,     (a)    What   velocity   did  it  acquire?     (6)    How 
high  is  the  cliff? 

3.  If  a  falling  body  has  acquired  a  velocity  of  150  feet  per  second, 
how  long  has  it  been  falling  ?     How  far  ? 

4.  How  many  centimeters  does  a  stone  fall  in  0.5  seconds  ? 

5.  How  many  centimeters  does  a  stone  fall  during  the  fifth  second  ? 

6.  A  rifle  is  fired  straight  up  with  a  muzzle  velocity  of  2000  feet 
per  second.     How  long  before  the  bullet  comes  down  again?     How 
high  will  it  go?     (Assume  that  air  resistance  is  negligible,  which  is 
far  from  true.) 

7.  A  baseball  is  thrown  up  in  the  air  and  reaches  the  ground  after 
4  seconds.     How  high  did  it  rise? 

8.  The  weight  of  a  pile  driver  drops  5  feet  at  first  and  later  15  feet. 
How  much  faster  is  it  moving  when  it  strikes  in  the  latter  case  than  in 
the  first  case  ? 

9.  A  body  is  thrown  vertically  upward  with  a  velocity  of  50  meters 
per  second.     With  what  velocity  will  it  pass  a  point  100  meters  from 
the  ground?     (HINT.  —  How  high  does  the  body  rise?) 

10.  A  weight  is  hung  from  the  top  of  the  Washington  Monument 
(555  feet).     What  is  the  period  of  such  a  pendulum? 

11.  The  length  of  a  pendulum  which  makes  a  single  swing  per  sec- 
ond in  a  certain  laboratory  is  found  to  be  99.3  centimeters.     Com- 
pute the  value  of  g  (cm. /sec.2)  for  that  place. 


. 


PROJECTILES  171 

142.  Projectiles.  A  baseball  or  golf  ball  in  flight,  a  bomb 
dropped  from  an  airplane,  a  rifle  bullet,  or  the  projectile  from 
a  great  gun  on  a  battleship  differs  from  a  freely  falling  body 
only  because  of  the  initial  velocity  imparted  to  it  by  the  pro- 
jecting mechanism.  0 

If  there  were  no  air  resistance  and  if  gravity  did  not  act  at  all,  the 
motion  of  a  projectile  would  be  very  simple.     It  would  move  straight 
on  in  whatever  direction  it  had  been 
started  and  with  an  unvarying  velocity. 
If,  starting  from   A    (Fig.   174),  it  was 
at  1  at  the  end  of  the  first  second,  then 
after  2  seconds  it  would  be  at  2,  after 
3  seconds  at  3,  and  so  on  in  the  straight 
line  A  B. 

The  motion  of  a  real  projectile  differs 

from  the  imaginary  motion  just  described   A  5     c~ 

in  two  respects.  In  the  first  place,  Fig.  174.  Path  of  projectile, 
gravity  begins  to  act  on  the  real  pro- 
jectile the  instant  it  leaves  the  impelling  mechanism,  and  it  begins 
to  fall  just  as  if  it  were  not  already  in  motion.  To  find  where  it 
would  be  (except  for  air  resistance)  at  the  end  of  say  the  third 
second,  we  have  only  to  compute  how  far  a  body  falling  freely  from 
rest  drops  in  3  seconds  (namely,  144  feet)  and  we  find  the  real  projectile 
|  at  3',  just  144  feet  below  3,  where  it  would  have  been  except  for  gravity. 
The  path  AC  of  figure  174  may  be  called  the  ideal  or  vacuum  trajec- 
tory (path)  of  the  projectile.  The  real  trajectory  AD  is  lower,  and 
^  steeper  on  the  descending  side,  because  of  air  resistance.  This  kills 
out  the  sidewise  motion,  so  that  the  projectile  takes  longer  and  longer 
to  cover  any  given  horizontal  distance  and  has  meanwhile  more  and 
more  time  to  fall. 

PROBLEMS 

(Neglect  air  resistance.) 

1.  A  rifle  is  fired  horizontally  from  the  top  of  a  cliff  which  is  144 
feet  high.     The  velocity  of  the  projectile  is  1200  feet  per  second, 
(a)    How  long  will  it  be  before  it  hits  the  ground?     (6)    How  far  does 
it  go  horizontally  ? 

2.  A  projectile  is  fired  with  a  velocity  of  144  feet  per  second  and 
at  an  angle  of  45°  to  the  horizontal.     Draw  a  diagram  to  show  its 


172 


Line  of  flight  of  Plane 
Ground  Speed  98. SSft^tee, 


'.at  5539  ft. 

Fig.    175.      Actual  path  of  bomb 
dropped  from  airplane. 


ACCELERATED  MOTION 

position  at  the  end  of  each  second. 
(Use  a  scale  £  inch  =  16  feet.)  Find 
(a)  the  greatest  height  reached  and 
(6)  the  horizontal  range. 

3.  Repeat    problem    2,     using     an 
angle  of  elevation  of  30°  to  the  hori- 
zontal. 

4.  Figure    175    shows    the    actual 
path  of  a  bomb  dropped  at  night  from 
an  airplane  during  a  test  at  Langley 
Field,  Va.,  during  the  war.     The  bomb 
carried    a  2000-candle-power  electric 
light    and    was    photographed    each 
second  with  two   cameras   2630   feet 
apart.     The  airplane  was  flying  hori- 
zontally at  a  speed  of  98.28  feet  per 
second,  and  the  bomb  moved  horizon- 
tally 1698  feet  in  the  first  18  seconds, 
and  dropped  4965  feet.    By  how  much 
did  the  actual  path  deviate  from  the 
theoretical  path? 

5.  The  bomb  of  the  last  problem 
moved  horizontally  875  feet  in  the  first 
9  seconds,  and  dropped  1287  feet.    Are 
these  distances  greater  or  less    than 
would  be  expected  in  comparison  with 
the  figures  for  18  seconds?     Why? 


SUMMARY   OF  PRINCIPLES  IN   CHAPTER  VII 

Average  speed  =  Distance 
time 

Acceleration  =  change  in  sPeed- 
time 

Laws  of  motion  at  constant  acceleration  starting  from  rest : 

at* 
1.     v  =  at.        II.    s  =  y-         III.   v2  =  2  as. 

Value  of  acceleration  of  gravity  : 

g  =  32.2  ft./sec.2  =  980  cm./sec.2. 
Projectile  combines  free  fall  with  straight  line  motion. 


PRACTICAL  EXERCISES 


QUESTIONS 


173 


1.  By  means   of   the   apparatus  shown  in  figure  176,  one  ball  is 
dropped  and  at  the  same  instant  another  is  thrown  horizontally. 
Which   strikes   the   floor 

first? 

2.  Find  out  what  Gali- 
leo observed  in  connection 
with  the  chandelier  in  the 
cathedral  at  Pisa. 

3.  How  must  the  pen- 
I  dulum  bob  be  moved  on 

a  clock  which  is  running 
too  fast  ? 


Fig.    176.     Apparatus  for   dropping  a  ball  and 
throwing  another  ball  at  the  same  instant. 


4.  What  is  the  difference  between  a  simple 
pendulum  and  a  compound  pendulum?     What 
is  meant  by  the  center  of  oscillation?   What  is 
the  center  of  percussion  of  a  baseball  bat  ? 

5.  Many   faucets    discharge    round,   smooth, 
quiet  streams  of  water.     Explain  why  the  diam- 
eter of  such  a  stream  is  smaller  at  the  bottom 
than  near  the  faucet. 

6.  What   other  factors  besides  air  resistance 
make  the  real  trajectory  of  a  projectile  deviate 
from  the  ideal  trajectory  ? 

PRACTICAL  EXERCISES 

1.  Acceleration  of  an  automobile.     By  means 
of  a  stop  watch  and  a  speedometer  measure  the 
positive  and  negative  acceleration  of  an  automo- 
bile under  varying  conditions.     If  possible,  try 
the  same  experiment  with  an  entirely  different 
type  of  automobile.     Discuss  your  results. 

2.  Use  of  pendulums  in  clocks.      Examine   a 
dissected  Swiss  or  other  pendulum  clock,  compar- 
ing what  you  find  with  figure  177.     How  does  the 
pendulum  control  the  movement  of  the  escape- 
ment wheel?    What  drives  this  wheel?    Examine 

if  you  can,  and  report  on  the  mechanism  of  a  clock  in  some  tower  or 
church  steeple. 


Fig.  177.  Escapement 
wheel  and  pendulum 
of  a  clock. 


CHAPTER  VIII 

THREE  LAWS   OF  MOTION 

Newton's   laws  —  inertia  —  the   fundamental   proportion 
of  force  and  acceleration  —  action  and  reaction  —  mass. 

143.  Newton's  laws  of  motion.     We  have  been  describing 
different  motions,  such  as  motion  at  constant  speed  and  motion 

at  constant  acceleration.  Now 
we  shall  try  to  explain  dif- 
ferent motions  by  studying  the 
forces  that  cause  them.  Prac- 
tically all  that  we  know  about 
this  part  of  physics  dates  back 
to  Sir  Isaac  Newton  (Fig.  178), 
who  in  1687  wrote  a  treatise 
on  the  principles  (Prindpia) 
of  natural  philosophy,  or  phys- 
ics. His  whole  book,  and  in- 
deed all  mechanics  since  his 
day,  is  based  on  three  very 
simple  laws,  called  Newton's 

Fig.    178.     Sir    Isaac    Newton     (1642-  laws.      The  first  of  them  is  the 

1727).     An  Englishman,  who  founded  ,  r  .         ..       ,,  ,    ,u 

the  science  of  mechanics,  and  made  law  ot  U*erfaa,  the   second  the 

many  important  discoveries  in  light.  law    of    acceleration,    and    the 

third   the   law    of    interaction.     These   will    be   discussed   in 
turn. 

144.  First  law  —  Inertia.     It  is  a  familiar  fact  that  nothing 
in  nature  will  either  start  or  stop  moving  of  itself.     Some 
force  from  outside  is  always  required.     For  example,  a  horse 
when  starting  a  wagon,  even  on  an  excellent  road,  has  to  pull 
very  hard  at  first ;  after  the  wagon  is  going,  the  horse  can  keep 

174 


INERTIA 


175 


Fig.  179.     Inertia  keeps  the 
ball  from  moving. 


it  moving  with  very  little  effort ;  but  if  he  tries  to  stop  it  to 
avoid  running  over  some  one,  he  has  to  push  back  hard.  So 
also  when  a  moving  ship  collides  with 
another  ship  or  a  dock,  it  requires  an 
enormous  retarding  force  to  stop  her. 
This  property,  which  all  matter  pos- 
sesses, of  resisting  any  attempt  to  start 
it  if  at  rest,  to  stop  it  if  in  motion,  or  in 
any  way  to  change  either  the  direction  or 
amount  of  its  motion,  is  called  inertia. 

We  may  illustrate  this  property  of  in- 
ertia by  balancing  a  card  on  a  finger  with 
a  coin  on  top  and  snapping  the  card  out, 
leaving  the  coin  on  the  finger.  The  coin  moves  only  a  little  because 
the  force,  due  to  friction,  is  too  small  to  get  it  started.  This  may 
also  be  done  with  the  apparatus  shown  in 
figure  179. 

Another  interesting  experiment  is  to  try 
to  pick  up  a  flatiron  by  means  of  a  linen 
thread  tied  to  it  (Fig.  180).  If  we  pull 
slowly,  we  may  be  able  to  do  it,  but  if  we 
pull  with  a  jerk,  the  thread  always  breaks, 
because  so  much  extra  force  is  required  to 
set  the  flatiron  in  motion  quickly. 

This  familiar  fact,  that  bodies  act 
as  if  disinclined  to  change  their  state 
whether  of  rest  or  of  motion,  was  ex- 
pressed by  Newton  in  the  following 
way: 

LAW  I.     Every    body     persists     in 
a  state  of  rest,  or  of  uniform  motion  in 
Fig.  180.    inertia  holds  the'  a  straight  line,  unless  compelled  by  ex- 
flatiron  still.  ternal  force  to  change  that  state. 

QUESTIONS 

1.    If  you  roll  a  ball  along  the  ground,  why  does  it  not  keep  going 
indefinitely  ? 


176  THREE  LAWS  OF  MOTION 

2.  Explain  how  an  automobile  provided  with  a  self-starter  con- 
forms to  Newton's  first  law. 

3.  One  often  sees  in  a  street  car  the  sign,  "Wait  till  the  car  stops." 
What  has  this  to  do  with  inertia? 

4.  If  a  moving  train  is  suddenly  stopped  by  the  emergency  brakes, 
in  which  direction  are  the  passengers  thrown?     Explain. 

5.  A  baseball  is  thrown  vertically  up  into  the  air.     Why  does  it 
not  keep  on  moving  in  a  straight  line  forever  ? 

146.    Applications  of  inertia.     A  nail  can  easily  be  driven  into  a 
heavy  piece  of  wood,  even  when  the  wood  does  not  lie  on  a  firm  founda- 
tion,  because  the  quick  blow 
of  a  hammer  does  not  set  the 
heavy  piece  of  wood  in  motion 
to   any   great    extent.     It    is 
very    difficult,     however,     to 
drive  a  nail   through  a  light 
stick  unless  the  stick  is  placed 
upon   a    solid    foundation,  or 
Fig.  181.    Inertia  of  sledge  hammer.         unless  the  stick  is  steadied  by 
the  inertia  of  a  heavy  sledge  hammer,  as  shown  in  figure  181. 

When  the  head  of  a  hammer  comes  off,  the  best  way  to  drive  it  on 
again  is  to  hit  the  other  end  of  the  handle,  rather  than  the  head,  against 
some  solid  foundation  or  with  another  hammer.  Why  ? 

146.  The  centrifugal  tendency.  The  tendency  of  a  body 
to  continue  to  move  in  a  straight  line  is  very  evident  when  it 
is  desirable  to  make  the  body  move  in  a  circle.  In  such  a  case, 
a  force  is  required  to  pull  the  body  in  toward  the  center  of  the 
circle,  so  that  it  will  not  fly  off  on  a  tangent.  Such  a  force  is 
called  a  centripetal  force,  meaning  a  force  directed  toward  the 
center. 

Thus,  when  an  automobile  takes  a  corner  at  any  considerable  speed, 
the  passengers  find  themselves  crowded  up  against  the  outside  cushions, 
which,  by  pushing  inward  against  them,  force  them  to  take  the  desired 
curved  path  through  space.  The  automobile  itself  has  to  be  pushed 
inward  by  the  friction  of  the  road  against  its  tires  if  it  is  to  take  the 
curve  safely.  If  the  road  is  so  slippery  that  it  cannot  exert  the  neces- 
sary inward  force,  the  automobile  skids,  that  is,  starts  to  fly  off  on  a 
tangent  to  the  desired  course. 


THE    CENTRIFUGAL    TENDENCY 


177 


When  an  athlete  swings  a  16-pound  hammer  around  his  head  before 
throwing  it,  he  has  to  pull  it  inward  because  of  its  inertia.  When  he 
stops  pulling  inward,  it  flies  off 
on  a  tangent.  So  all  he  has  to 
do  to  throw  it  is  to  let  go. 

Grinding  wheels  revolve  very 
rapidly.  Sometimes  one  bursts 
because  the  cohesion  between  its 
parts  is  not  enough  to  supply  the 
centripetal  force  necessary  to  keep 
these  various  parts  moving  in 
their  respective  circles. 

The  mud  on  a  bicycle  wheel 
stays  on  the  wheel  only  if  the 
adhesion  between  it  and  the  tire 

is  great  enough  to  pull  it  around     <   

with  the  tire;  otherwise  it  flies  off     lg>       ' 
on  a  tangent  (Fig.  182). 

In  a  cream  separator  (Fig.  183)  the  denser  part  of  the  milk  gets 
outside  and  crowds  the  lighter  cream  inward.     This  is  because   the 


Skim-milk  Outlet 


Cream  Outlet 
Skim-milk  Outlet 


Fig.  183.    A  cream  separator  and  diagram  of  the  rotating  disks. 

greater  inertia  of  the  milk  (that  is,  its  greater  tendency  to  move  along 
a  tangent)  prevails  over  that  of  the  cream.  The  conical-shaped  disks 
rotate  very  rapidly  and  so  whirl  the  milk  at  a  high  speed. 


178 


THREE  LAWS  OF  MOTION 


Electri. 
Moto 


All  these  cases  show  the  centrifugal  tendency,  that  is,  the 
tendency  to  fly  out  from  the  center  along  a  tangent,  which  every- 
thing manifests  when  made  to  follow  a  curved  path. 

Machines  which  make  use  of  the  centrifugal  tendency  to  separate 
one  kind  of  thing  from  another  are  often  called  centrifuges.  Thus 

the  mother  liquor  is  driven  away  from 
the  crystallized  sugar  in  refineries 
(Fig.  184),  and  the  water  is  driven 
out  of  clothes  in  laundries,  in  rapidly 
rotating  perforated  baskets. 

147.  Second  law  —  Accelera- 
tion. We  have  been  discussing 
what  happens  to  a  body  when 
forces  do  not  act  on  it.  Let  us 
now  consider  what  happens  when 
forces  do  act  on  it. 

Whenever  an  "  unbalanced  " 
force  is  acting^pn  a  body,  the 
body  has  an  acceleration  in  the 
direction  in  which  the  force  acts, 
and  the  acceleration  is  proportional  to  the  force.  An  unbalanced 
force  means  more  push  or  pull  in  one  direction  than  in  the  other. 
Thus,  suppose  a  locomotive  is  pulling  a  train  at  a  constant  speed 
of  50  miles  an  hour.  The  engine  is  certainly  exerting  a  force  on  the 
train;  but  there  are  other  forces,  due  to  friction  and  air  resistance, 
acting  in  the  opposite  direction,  and  these  just  balance  the  pull  of.  the 
engine.  The  net  force  forward  is  zero  ;  if  it  were  not  zero,  the  train 
would  not  only  be  going  forward  but  accelerating  forward  ;  it  would  be 
gaining  speed.  It  is  important  to  keep  in  mind  that  it  is  net  force  and 
acceleration  which  always  go  together,  and  not  net  force  and  motion. 

LAW  II.  The  acceleration  of  a  given  body  is  proportional  to 
the  force  causing  it. 

That  is,  if  any  given  body  is  acted  on  at  one  time  by  a  force 
Fij  and  at  another  time  by  another  force  F2,  then 


Fig.  184.     Sugar  centrifuge  used  to 
separate  sirup  from  sugar  crystals. 


where  ai  and  a2  are  the  accelerations  produced  by  FI  and  F2. 


ACCELERATION  179 

Thus,  if  we  push  an  automobile  with  a  certain  force,  and 
at  another  time  push  it  twice  as  hard,  it  will  have  twice  as 
much  acceleration  the  second  time  as  the  first. 

One  way  to  cause  a  force  to  act  on  a  body  is  to  let  the  body 
fall.  In  this  case  the  force  acting  is  known,  for  it  is  the  weight 
W  of  the  body.  The  acceleration  is  also  known,  for  it  is  gr,  which 
is  32.2  feet-per-second  per  second,  or  980  centimeters-per-sec- 
ond  per  second.  So  the  weight  of  the  body  and  its  acceleration 
when  falling  can  always  be  used  as  two  of  the  numbers  in  the 
proportion  just  mentioned. 

That  is,  |-J. 

This  enables  us  to  compute  the  force  needed  to  give  a  cer- 
tain body  any  desired  acceleration. 

FOR  EXAMPLE,  a  freight  train  weighs  1000  tons.  How  great  a  force 
is  necessary  to  give  it  an  acceleration  of  half  a  foot-per-second  per 
second  ? 

F    ^0.5 
1000  "32.2 


148.  Consistent  Units.  In  the  equation  F/W  =  a/g,  it 
makes  no  difference  in  what  unit  F  and  W  are  expressed,  pro- 
vided only  that  both  are  expressed  in  the  same  unit.  Both  can  be 
expressed  in  pounds,  or  in  ounces,  or  in  tons,  or  in  kilograms, 
or  in  grams,  or  in  a  less  familiar  unit  called  a  "  dyne."  The 
dyne  is  a  very  small  unit  of  force  sometimes  used  in  scientific 
work.  It  can  be  defined  as  1/980  of  a  gram  weight.*  It  is 
about  the  weight  of  a  milligram.  If  a  force  is  given  in  terms 
of  any  one  of  these  units,  it  can  be  expressed  in  terms  of  any 
other  of  them  with  the  help  of  the  following  table  : 

1  gram     =  980  d.ynes.  1  dyne   =  0.00102  grams. 

1  pound  =  454  grams.  1  gram  =  0.00220  pounds. 

1  pound  =  445,000  dynes.  1  dyne  =  0.00000225  pounds. 

*  See  also  problems  4.  and  5,  page  180. 


180  THREE  LAWS  OF  MOTION 

Similarly,  a  and  g  may  be  expressed  in  any  unit,  provided 
only  that  both  are  expressed  in  the  same  unit.  If  both  are  to  be 
in  feet-per-second  per  second,  the  numerical  value  of  g  is  32.2 ; 
if  both  are  to  be  in  centimeters-per-second  per  second,  the 
numerical  value  of  g  is  980. 

PROBLEMS 

(In  these  problems  use  32  ft. /sec2,  or  980  cm. /sec2,  for  g.) 

1.  What  acceleration  will  a  force  of  5  pounds  produce  in  a  body 
weighing  16  pounds? 

2.  What  acceleration  will  a  force  of  1  gram  produce  in  a  body 
weighing  490  grams  ? 

3.  What  acceleration  will  a  force  of  1  pound  produce  in  a  body 
weighing  1  pound? 

4.  What  acceleration  will  a  force  of  1  dyne  produce  in  a  body 
weighing  1  gram  ?     (NOTE.  —  The  answer  to  this  problem  is  often 
regarded  as  the  definition  of  a  dyne.) 

6.    State  accurately  in  words  the  definition  of  a^dyne  that  is  referred 
to  in  the  last  problem. 

6.  A  body  weighing  10  pounds  is  observed  to  have  an  acceleration 
of  2  feet-per-second  per  second.     What  force  is  acting  ? 

7.  A  force  of  1  kilogram  is  observed  to  produce  an  acceleration 
of  9.8  meters-per-second  per  second  in  a  certain  body.     How  much 
does  the  body  weigh? 

«*:  A  force  of  1000  dynes  is  observed  to  produce  an  acceleration 
of  9.8  centimeters-per-second  per  second  in  a  certain  body.  How  many 
grams  does  the  body  weigh?  F  *  »<  ***-  \  i*+*  '  I  X  *1  X  T»f / 

9.   An  automobile  weighing  2  tons  is  started  from  rest  with  an  - 
acceleration  of  4  feet-per-second  per  second.     How  hard  is  the  road 
pushing  forward  on  the  bottoms  of  the  rear  tires  ? 
\  ,10.   A  train  starting  from  rest  with  a  constant  acceleration  takes  44 
seconds  to  get  up  to  a  speed  of  30  miles  an  hour.     If  the  train  consists 
of  10  all-steel  cars,  each  weighing  64  tons,  what  pull  is  exerted  by  the 
e'ngine?     (HINT.  —  Compute  acceleration  and  then  find  force.)   "V  •  ^  ^ 

149.  Third  law  —  Interaction.  Newton's  third  law  is  based 
on  two  familiar  facts.  One  way  of  stating  the  first  of  these 
facts  is  that  there  can  never  be  a  force  acting  in  nature  unless 


INTERACTION  181 

two  bodies  are  involved,  one  exerting  it  and  one  on  which  it 
is  exerted.  Thus,  when  a  railroad  train  is  pulled,  there  is  an 
engine  that  does  the  pulling;  and  on  the  other  hand,  the  en- 
gine cannot  exert  a  pull  or  a  push  unless  there  is  something  to 
be  pulled  or  pushed.  An  electric  car  or  an  automobile  seems, 
perhaps,  to  push  itself  along,  but  really  the  track  or  the  road 
under  the  wheels  is  exerting  a  force  on  the  wheels  and  pushing 
the  car  forward.  We  have  all  seen  what  happens  when  the 
car  track  is  so  icy  or  the  road  so  muddy  that  it  cannot  push  on 
the  wheels.  The  motor  is  going  just  as  hard  as  ever,  but  the 
car  does  not  move.  Another  case  is  that  of  any  heavy  object : 
there  is  a  force  called  its  weight  (force  of  gravity)  pulling  it 
down ;  but  we  know  that  it  is  the  earth  that  exerts  this  force. 

This,  then,  is  the  first  fact :  whenever  there  is  a  force  in  nature 
there  must  be  two  bodies,  one  to  exert  it  and  one  to  receive  it. 

But  we  can  go  further  than  this.  We  can  say  that  when- 
ever there  is  a  force  in  nature  there  must  be  not  only  two  bodies 
involved,  but  another 
force.  That  is,  forces 
never  exist  singly,  but 
always  in  pairs.  If  the 
first  force  is  exerted  by 
a  locomotive  on  a  train, 

the  second  will  be  exerted 

—  ^TV. 

by  the  train  on  the  loco- 
motive.     The   train  will       **• '«5.    Track  pushes  the  engine  forward. 

pull  back  on  the  locomotive  just  as  hard  as  the  locomotive  pulls 
forward  on  the  train.  If  a  road  is  pushing  forward  on  the  wheels 
of  the  automobile,  the  wheels  must  be  pushing  back  on  the  road. 
In  order  to  make  this  idea  seem  more  real  to  us,  let  us  try  the  ex- 
periment on  a  small  scale,  as  shown  in  figure  185.  If  we  wind  up  the 
little  toy  engine  and  place  it  on  the  circular  track,  which  is  so  mounted 
as  to  turn  easily,  we  find  that  the  track  turns  around  and  the  rails 
under  the  wheels  go  backwards.  If  we  hold  the  track  fast,  the  engine 
goes  ahead  faster  than  at  first;  and  if  we  hold  the  engine  fast,  the 
track  turns  around  backwards  faster  than  at  first. 


o 


182  THREE  LAWS  OF  MOTION 

Finally,  when  any  heavy  object  is  pulled  downward  by  the 
earth,  the  heavy  object  must  be  pulling  the  earth  up  with  an 
equal  force.  This  does  not  seem  very  likely  at  first,  but  that 
is  simply  because  the  force  is  usually  so  small  and  the  earth  so 

large  that  the  force  has  an 
imperceptible  effect  on  the 
earth.  In  the  case  of  a 
heavy  body  as  large  as  the 
moon,  the  effect  is,  however, 
quite  perceptible  to  astrono- 
mers. The  earth  and  the 

moon   are   actually   rotating 
Rotation  of ^the  moon  about  the  about      ft       point      Q       (pig> 

186),  which  is  not  exactly 
at  the  center  of  the  earth.  So  the  moon  must  continually 
pull  the  earth  to  make  its  center  of  gravity  move  in  its 
circle. 

This  fact  that  forces  always  occur  in  pairs,  one  force  of  each 
pair  being  equal  and  opposite  to  the  other,  was  expressed  by 
Newton  in  the  following  form : 

LAW  III.  With  every  action  (or  force)  there  is  an  equal  and 
opposite  reaction. 

150.  Universal  gravitation.  The  fact  that  the  earth  and 
the  moon  attract  each  other  is  only  one  example  of  a  very  gen- 
eral law,  also  discovered  by  Newton,  called  the  law  of  universal 
gravitation.  According  to  this  law  every  material  thing  in 
the  universe  attracts,  and  is  attracted  by,  every  other  material 
thing.  When  we  lay  two  bricks  near  each  other  on  a  table, 
each  pulls  the  other,  but  the  force  is  so  tiny  that  nobody  notices 
it.  Yet  the  attraction  of  the  sun  for  the  earth,  and  also  that  of 
the  earth  for  the  sun,  which  are  forces  of  exactly  the  same 
kind,  amount  to  over  1024  (that  is,  1  followed  by  24  zeros) 
tons,  because  the  sun  and  the  earth  both  contain  so  much 
matter. 

In  general,  the  attraction  between  any  two  bodies  is  pro- 


MASS   VS.    WEIGHT  183 

portional  to  the  amount  of  matter  in  each  of  them,  and  inversely 

proportional  to  the  square  of  the 

distance  between  them;   that  is, 

the  attraction  is  reduced  to  a 

quarter   when   the    distance   is 

doubled,  and  to  one  ninth  when 

the  distance  is  trebled. 

151.  Mass  vs.  weight. 
"  Mass  "  and  "  weight"  are 
constantly  confused  in  ordi- 
nary conversation.  While  we 
have  preferred  not  to  use  the 
term  "  mass  "  in  studying  New- 
ton's second  law,  yet  it  is  well  to 
know  its  precise  meaning  so  that  Fie- 187-  standard  kilogram, 
one  can  read  intelligently  the  books  which  make  use  of  it. 

Mass  means  quantity  of  matter.  It  is  the  answer  to  the 
question,  "  How  much  matter  is  there  in  a  given  body?  " 

Weight  means  the  pull  of  gravity  on  the  body.  The  weight 
of  a  body  is  a  force  acting  on  the  body,  not  a  description  of 
what  it  contains. 

The  unit  of  mass  is  the  quantity  of  matter  contained  in  a 
certain  piece  of  platinum  (the  standard  kilogram,  Fig.  187). 

The  unit  of  weight  is  the  pull  of  the  earth  on  that  same 
piece  of  platinum,  when  it  is  near  sea-level  and  at  latitude  45°. 

Since  a  kilogram  mass  weighs  a  kilogram  under  these  stand- 
ard conditions,  the  mass  and  the  "  standard  weight  "  of  a  body 
are  numerically  equal.  But  if  we  carry  a  kilogram  mass  to  the 
top  of  a  high  mountain,  and  weigh  it  on  a  very  sensitive  spring 
balance,  it  will  weigh  less  than  a  kilogram,  because  it  is  farther 
from  the  center  of  the  earth,  and  so  the  earth  pulls  less  hard  on 
it.  The  reading  of  the  spring  balance  might  be  called  its  "  local 
weight." 

Since  all  bodies  on  the  mountain  top  would  weigh  less  in  the 
same  proportion,  we  can  get  the  standard  weight  of  anything 


184  THREE  LAWS  OF  MOTION 

without  descending  the  mountain  by  weighing  it  on  an  equal- 
arm  balance  against  a  set  of  "  standard  weights."  This  is 
what  we  always  do  in  the  laboratory  and  in  the  outside  world 
when  we  want  to  know  weights  accurately.  So,  when  we  speak 
of  the  weight  of  a  body,  we  almost  always  mean  its  "  standard 

weight." 

W 
Since  F  =  — a,  and  since  the  standard  weight  W  and  the 

y 

mass  M  are  numerically  equal,  we  shall  get  the  same  value  for 
F  if  we  write  (when  using  grams,  centimeters,  and  seconds) 

Ma 

980 

or  980  F  =  Ma. 

Here  F  is  in  grams;  if  we  choose,  however,  to  express  the 
force  as  F'  dynes,  instead  of  as  F  grams,  then  F  and  F'  will 
be  different  numbers,  and 

F'  =  980  F 


so 


F    =  y»u  r 

•  F'  (dynes)  =  M  (grams)  X  a  (cm./sec.2). 

This  is  another  way  of  expressing  Newton's  second  law. 


SUMMARY  OF  PRINCIPLES   IN   CHAPTER  VIII 

Newton's  laws  of  motion  and  the  fundamental  proportion : 
I.    Every  body  continues  in  a  state  of  rest  or  of  uniform  mo- 
tion in  a  straight  line,   unless   compelled  by   external 
forces  to  change  that  state. 

II.   The  acceleration  of   a  given  body  is  proportional  to  the 
force  causing  it.          p        fl 

W  =  7 

III.    With  every  action  (or  force)  there  is  an  equal  and  opposite 

reaction. 

Mass  means  quantity  of  matter  in  a  given  body. 
Weight  means  the  pull  of  gravity  on  the  body. 


QUESTIONS 


185 


QUESTIONS 

1.  Why  does  a  train  continue  to  move  after  the  steam  is  shut  off? 

2.  What  does  an  aviator  have  to  do  to  round  a  corner  safely,  and 
why? 

3.  Why     can     small     grinding 
wheels  be  safely  driven  at  a  greater 
speed,  that  is,  at  more  revolutions 
per  minute,  than  larger  ones  ? 

4.  Why  does  a  wheel,    or   any 
revolving  part  of  a  machine,  some- 
times shake  or  hammer  in  its  bear- 
ings? 

5.  Explain    how    a    locomotive 
engineer  can  tell,  when  he  starts  up 
his  train,  if  one  of  the  cars  has  been 
uncoupled  from  the  train. 

6.  Why  is  an  indoor  running  track  "banked"  at  the  turns?     Why 
is  a  railroad  track  banked  on  the  curves?     Study  figure  188,  where  A 
is  the  upward  push  on  the-  wheels,  B  is  the  centripetal  force  exerted 
inward  by  the  rails,  and  R  is  the  resultant. 

7.  Are  the  automobile  trunk  line  roads  banked  on  the  curves  in 
your  state? 

8.  Explain  the  working  principle  involved  in  a  centrifugal  pump. 
See  figures  119  and  120. 

PRACTICAL  EXERCISE 

Looping  the  loop.  Construct  a  working  model  to  illustrate  the 
circus  performance  called  "  looping  the  loop."  State  the  principles 
involved. 


Fig.  188.     Banking  rails  on  a  curve. 


CHAPTER  IX 

POTENTIAL  AND   KINETIC  ENERGY 

Energy  —  potential  energy  —  how  computed  —  kinetic  energy 
—  how  computed  —  transformation  of  energy  —  law  of  con- 
servation of  energy. 

152.  Energy.     When  a  pile  is  to  be  driven  into  the  ground, 
a  heavy  weight  is  lifted  and  allowed  to  drop  on  the  end  of  the 
pile  (Fig.  189).     Work  is  done  in  lifting  the  heavy  weight,  and 

as  a  result  it  can  doivork,  namely,  drive  the 
pile  into  the  ground.  This  capacity  of  the 
weight  in  its  elevated  position  to  do  work 
we  call  energy. 

If  we  use  a  heavier  weight  or  lift  it  to 
a  greater  height,  we  do  more  work  upon 
it,  and  as  a  result  the  weight  has  more 
energy  and  will  drive  the  pile  farther  into 
the  ground. 

The  water  rushing  out  of  the  nozzle  of 
a  Pelton  water  wheel  (section  79)  has  a 
great  capacity  for  doing  work  on  account 
-:O=     of  its  rapid  motion,  and  thus  has  energy. 
Fig.    189.     Pile   driver  The   greater  the   quantity  of  water  and 

hammering  a  log  into      .  .  .  %       « 

the  ground.  the  more  rapid  its  flow,  the  larger  is  the 

amount  of  energy  available. 

In  general,  the  energy  of  anything  may  be  denned  as  its 
capacity  for  doing  work. 

153.  Potential  energy.     The  water  above  the  falls  at  Niagara 
has  great  capacity  for  doing  work,  by  acting  on  suitable  tur- 
bine wheels,  because  of  its  vast  quantity  and  its  elevated  posi- 
tion.    When  a  clock  or  watch  spring  is  wound    up,    it  can 
drive  the  clock  as  it  uncoils  because  of  the  elastic  strain  within 

186 


POTENTIAL   ENERGY 


187 


it  due  to  its  change  in  shape.  The  energy  that  a  body  has  on 
account  of  its  position  or  state  of  strain  is  called  potential  energy. 
Thus  the  energy  of  the  hammer  of  the  pile  driver  when  raised 
is  potential.  The  energy  of  the  hot  compressed  gases  in  the 
cylinder  of  a  gas  engine,  just  after  the  explosion,  is  potential 
energy. 

154.  How  to  compute  potential  energy.     In  the  case  of  the 
pile  driver,  the  potential  energy  of  the  hammer  depends  on  its 
weight  and  on  the  height  to  which  it  is  raised.     In  other  words, 
the  potential  energy  of  the  hammer  is  found  by  comput  ng  the 
work  that  has  been  done  to  place  it  in  its  elevated  position. 
In  symbols, 

P.  E.  =  W  X  h 

where  W  is  the  weight  of  the  body  and  h  is  the  vertical  distance 
through  which  it  has  been  raised.  Potential  energy  (P.  E.)  is 
expressed  in  the  same  units  as  work. 

FOR  EXAMPLE,  suppose  the  hammer  of  a  pile  driver  weighs  3000 
pounds  and  is  lifted  12  feet ;  then  the  potential  energy  is  3000  X  12, 
or  36,000  foot  pounds,  or  18  foot  tons. 

155.  Kinetic  energy.     As  the  hammer  of  a  pile  driver  is 
allowed  to  drop,  it  gradually  loses  its  potential  energy,  but 
gains  more  and  more  of  another  kind  of  energy  as  its  speed 
increases.     Finally,  just  as  it  hits  the  pile,  the  potential  energy 
has  all  been  converted 

into  energy  of  mo- 
tion, which  is  called 
kinetic  energy. 

A  heavy  flywheel 
(Fig.  190)  will  keep 
machinery  running 
for  some  time  after 
the  power  has  been 
shut  off,  and  there- 
fore, because  of  its  p.g  igo  Flywheels  on  a  gas  engine  when  in  motion 

motion,     it     Can      do  have  kinetic  energy. 


Flywheels,. 


188  POTENTIAL  AND  KINETIC  ENERGY 

work.  The  engine  had  to  do  work  on  the  flywheel  to  get  it 
up  to  speed,  and  the  flywheel,  as  long  as  it  is  moving,  can  do 
work  on  the  shaft.  The  faster  and  heavier  the  flywheel,  the 
more  work  it  can  do  before  it  comes  to  rest. 

Every  body  in  motion  has  kinetic  energy;  that  is,  it  will  do 
a  certain  amount  of  work  against  a  resisting  force  before  it  stops 
moving. 

156  How  to  compute  kinetic  energy.  To  compute  how 
much  work  a  moving  body  can  do  against  a  retarding  force  be- 
fore it  comes  to  rest,  we  reverse  the  problem  and  compute  how 
much  work  must  be  done  to  start  the  body  and  get  it  up  to 
the  given  speed. 

The  fundamental  equation  for  the  work  done  by  any  force  F  acting 
through  a  distance  s  is 

Work  =  Fs. 

But  we  have  already  (section  147)  seen  that  the  force  F  necessary  to 
get  a  body  whose  weight  is  W  started  with  a  given  acceleration  a  may 
be  expressed  by  the  equation, 

F-*a. 

g 

Therefore,  the  work  done  is 


But  the  product  'as  can  be  expressed  in  terms  of  the  speed  v  by  means 
of  the  third  law  of  accelerated  motion  (section  136). 

Thus,  y2=2  as,  or  as  =  -- 


Fs-?™ 
~' 


So  the  work  done  is 


Therefore,  Kinetic  Energy  =  - 

In  using  this  equation  we  must  be  consistent  in  our  units.  For 
example,  F  and  W  are  both  forces  and  must  both  be  expressed  in  the 
same  unit.  Likewise,  s,  v,  and  g  must  all  involve  the  same  unit  of 
length.  In  expressing  the  velocity  v,  and  the  acceleration  g,  it  is  cus- 
tomary to  use  the  second  as  the  unit  of  time. 


KINETIC  ENERGY  189 

There  are  several  units  of  work  in  common  use,  such  as  the 
foot  pound  (ft.  lb.), 
foot  ton  (ft.  T.), 
gram  centimeter  (g.  cm.), 
kilogram  meter  (kg.  m.),  and 
dyne-centimeter  ("  erg  ").* 

Since  each  of  these  work  units  is  a  force  unit  times  a  distance  unit, 
we  can  always  tell  what  the  unit  of  kinetic  energy  is  if  we  notice  what 
force  unit  and  what  distance  unit  were  used  in  expressing  W,  v  and  g. 

157.  Applications    of    the    kinetic    energy    equation.     This 
equation  will  help  us  to  solve  many  useful  problems  about 
moving  things  which  involve  the  idea  of  distance. 

FOR  EXAMPLE,  suppose  a  2500-pound  automobile  running  30  miles 
an  hour  is  stopped  in  90  feet.     What  braking  force  is  applied? 
The  speed  30  miles  an  hour  =  44  ft. /sec. 
Then,  substituting  in  the  kinetic  energy  equation, 

2500  X  (44)' 

2  X  32.2 
and  F  =  835  Ibs. 

Again,  suppose  the  hammer  of  a  pile  driver  weighs  1500  pounds. 
It  falls  20  feet  upon  the  head  of  a  pile  and  drives  it  18  inches  into  the 
ground.  What  is  the  kinetic  energy  of  the  blow  delivered  to  the  pile? 
What  is  the  average  resistance  offered  by  the  ground? 

The  velocity  of  the  hammer  when  it  hits  the  pile  is  computed  from 
w2  =  2  gs  =  2  X  32.2  X  20. 

Therefore,  K.  B.  =  15°°  X  \  ^  X  2° 

=  30,000  ft.  Ibs. 

Note  that  the  kinetic  energy  of  the  moving  hammer  when  it  hits  the 
pile  is  equal  to  the  potential  energy  of  the  uplifted  hammer. 
If  the  average  resistance  is  called  F,  we  have 

F  X  1.5  =  30,000  ft.  Ibs. 
F  =  20,000  Ibs. 

158.  Kinetic  energy  different  from  momentum.     There  is  another 
property  of  moving  bodies  which  is  often  confused  with  kinetic  energy. 

It  is  called  momentum.    Its  value  is  — ,  while  kinetic  energy  is  -~ — 

*  The  dyne-centimeter  is  usually  called  an  erg ;  since  it  is  a  very  small  unit  of 
work,  the  joule  =  107  ergs  is  often  used  instead. 


190  POTENTIAL  AND  KINETIC  ENERGY 

The  amount  of  momentum  that  an  accelerating  body  gains  per  sec- 
ond is  a  measure  of  the  net  force  acting.  To  prove  this,  w^  notice 
that  if  the  body  starts  from  rest,  the  gain  in  momentum  per  second 

is  — rg     But  7  is  the  acceleration  a,  and  — -  is  equal  to  the  net  force 
gt  t  g 

acting  (section  147). 

Also,  the  amount  of  momentum  a  moving  body  has  is  an  indication 
of  how  long  it  will  move  against  a  given  resistance ;  just  as  its  kinetic 
energy  indicates  how  far  it  will  move  before  it  stops.  To  prove  this, 

we  notice  that  Ft  = One  should  be  careful  not  to  say  "  momen- 
tum" when  one  really  means  kinetic  energy,  or  "  energy  "  when  one 
means  momentum. 

PROBLEMS 

(State  the  unit  in  which  each  answer  is  expressed.) 

1.  What  is  the  kinetic  energy  of  a  baseball  weighing  one  third  of  a 
pound  if  its  velocity  is  64  feet  per  second  ? 

2.  What  is  the  kinetic  energy  of  a  150-ton  locomotive  going  60 
miles  an  hour? 

3.  What  is  the  kinetic  energy  of  a  9.8-kilogram  weight  which  has 
been  falling  long  enough  to  have  a  velocity  of  12  meters  per  second? 

4.  What  is  the  kinetic  energy  of  a  16-gram  bullet  whose  velocity 
is  600  meters  per  second? 

6.    Find  the  kinetic  energy  in  ergs  of  a  stone  weighing  20  grams  when 
it  is  thrown  with  a  velocity  of  800  centimeters  per  second. 

6.  The  14-inch  guns  on  some  of  the  United  States  warships  fire  a 
projectile  weighing  1400  pounds  and  are  said  to  give  it  a  "muzzle 
energy"  of  65,600  foot  tons.     What  is  the  velocity  of  the  projectile  as 
it  leaves  the  gun  ? 

7.  What  resistance  is  necessary  to  stop  a  body  whose  kinetic  energy 
is  90,000  ergs,  in  a  distance  of  3  meters  ? 

8.  A  boy  weighing  100  pounds  starts  to  slide  on  ice  at  a  speed  of  20 
feet  per  second.    What  is  his  initial  energy?     If  the  retarding  force  due 
to  friction  is  40  pounds,  how  far  will  he  go  before  stopping? 

9.  How  great  a  force  in  excess  of  that  required  to  overcome  friction 
is  necessary  to  bring  a  3200-pound  automobile  up  to  a  speed  of  30  miles 
an  hour  in  a  distance  of  242  feet  ? 

10.  A  2-ounce  bullet  is  shot  vertically  into  the  air  with  a  velocity 
of  1200  feet  per  second.  How  much  and  what  kind  of  energy  does  it 


THE  CONSERVATION   OF  ENERGY 


191 


have   (a)    as  it  leaves  the  gun? 
it  reaches  the  highest  point  ? 


(6)    10  seconds  later?     (c)    when 


159.  Transformation  of  energy.     In  nature  kinetic  and  poten- 
tial forms  of  energy  are  continually  changing  into  one  another. 

Thus,  when  a  pendulum  bob  (Fig.  191)  is  at  the  highest  part  of  its 
swing  A,  it  has  potential  energy  because  of  its  height  h.  As  it  swings 
down,  this  potential  energy 
disappears  ;  but  the  bob  gains 
speed,  and  at  B  its  energy  is 
all  kinetic.  As  the  bob  swings 
up  again  on  the  other  side  C, 
its  velocity  and  kinetic  en- 
ergy decrease,  but  its  po- 
tential energy  increases.  At 
C  its  energy  is  all  potential 
and  equal  to  that  at  A,  if 
there  are  no  losses  due  to 
friction. 

Similarly,  when  the  ham- 
mer of  a  pile  driver  is  at  its 
highest  position,  its  energy  is 

all  potential.      When  it  hits     ^^^  ^-^_     ^^       _,---'1^P^    }h 
the  pile,  it  has  lost  this  poten- 
tial energy,  but  has  gained 
an  equal  amount  of  kinetic    Fig.   191. 
energy. 

160.  The  conservation  of  energy.     As  these  examples  indi- 
cate, energy  is  never  made  from  anything  that  is  not  energy, 
or  turned  into  anything  that  is  not  energy.     The  total  quantity 
of  energy  in  the  universe  is  always  the  same  and  is  changed 
only  in  form  and  distribution.     In  any  given  machine  there 
may  be  leaks  of  energy  because  of  friction,  radiation,  etc. ; 
however,  the  energy  that  leaks  away  is  not  destroyed,  but  is 
given  as  heat  to  the  surroundings  of  the  machine. 

Thus,  in  the  pendulum  (Fig.  191)  the  sum  of  the  kinetic  and  po- 
tential energies  is  the  same  wherever  it  is  in  its  swing,  unless  there  is 
friction.  If  there  is  friction,  some  energy  disappears  as  heat  and  less 
is  left  in  the  pendulum ;  but  the  total  energy  is  unchanged. 


Transformation  of   energy   in  a 
pendulum. 


192 


POTENTIAL   AND  KINETIC  ENERGY 


Whenever  one  form  of  energy  disappears,  other  forms  appear 
in  equivalent  amounts.     This  fact,  that  energy  can  never  be 

manufactured  or  destroyed,  but 
only  transformed  or  directed 
in  its  flow,  was  first  stated 
(not  very  clearly)  by  a  Ger- 
man, Robert  Mayer,  and  was 
firmly  established  by  Helm- 
holt  z.  It  is  called  the  LAW 

OF     THE     CONSERVATION     OF 

ENERGY  and  has  become  the 
most  important  generaliza- 
tion in  all  physics. 

161.  Dissipation  of  en- 
ergy. When  energy  is  used 
or  transformed,  although 
none  is  ever  destroyed, 
there  is  always  a  loss  of 
another  kind.  Thus  when 
mechanical  energy  is  used  to 
drive  a  machine  and  the  ma- 
chine in  turn  does  work,  as 
in  lifting  something,  the  out- 
put of  the  machine  is  less  than  the  input  because  of  friction. 
The  balance  of  the  energy  put  in  is  changed  into  heat,  and  dif- 
fused or  dissipated,  so  that  it  is  no  longer  useful  energy.  The 
loss  is  not  in  the  total  quantity  of  energy  in  the  world,  but  in 
the  usefulness  or  availability  of  some  of  it.  The  same  is  true 
whenever  mechanical  or  chemical  energy  is  changed  into  elec- 
trical, or  when  electrical  or  thermal  energy  is  changed  into 
mechanical.  Lord  Kelvin  (Fig.  192)  was  one  of  the  first  to 
recognize  the  general  principle  that  whenever  energy  is  used  or 
transformed,  some  of  it  slips  from  our  control  and  becomes  for- 
ever dissipated  and  unavailable. 


Fig.  1 92 .  Lord  Kelvin  ( Sir  William  Thom- 
son, 1824-1907).  Professor  of  physics 
in  Glasgow  University  for  more  than 
fifty  years.  Eminent  electrical  engineer. 
Made  Atlantic  cables  work.  A  pioneer 
in  the  development  of  thermodynamics. 


SUMMARY  193 

SUMMARY   OF  PRINCIPLES   IN   CHAPTER  IX 

Energy  of  a  body  is  its  capacity  for  doing  work. 
Units  of  energy  same  as  units  of  work. 
Potential  energy  =  Wh. 

Wv* 
Kinetic    energy  =  -= — 

The  conservation  of  energy :  Energy  can  never  be  manufac- 
tured or  destroyed,  but  only  transformed  or  directed  in  its 
flow. 

QUESTIONS  AND  PROBLEMS 

1.  Trace  the  transformations  of  energy  in  the  process  of  firing  a 
gun. 

2.  Trace  the  transformations  of  energy  when  water  from  a  mill 
pond  drives  an  overshot  water  wheel  and  the  power  obtained  is  used 
to  run  a  sawmill. 

3.  In  what  form  is  energy  supplied  to  a  man?   to  a  horse?   to  an 
automobile  ?  to  a  locomotive  ? 

4.  The  pendulum  of  a  clock  would  die  down  because  of  the  friction 
of  the  air  around  it  if  energy  were  not  continually  supplied  to  it.     How 
is  this  done? 

6.  A  certain  rifle  was  once  described  in  the  headline  of  a  maga- 
zine advertisement  as  striking  ' '  a  blow  of  2038  pounds. ' '  Farther  down 
in  the  advertisement  it  appeared  that  the  bullet  weighed  -^  of  a  pound, 
and  that  its  velocity  was  2142  feet  per  second.  What  did  the  headline 
mean? 

6.  A  1-pound  ball  falls  for  two  seconds  and  rebounds  a  distance 
of  50  feet.  How  much  mechanical  energy  has  the  ball  lost?  What 
has  become  of  the  lost  energy  ? 

PRACTICAL  EXERCISE 

Perpetual-motion  machines.  Consult  an  encyclopedia  on  per- 
petual-motion machines.  Describe  how  some  of  them  are  supposed 
to  operate  and  explain  the  fallacy  in  their  construction. 


CHAPTER   X 
HEAT— EXPANSION   AND  TRANSMISSION 

Thermometer  scales  —  linear  and  volumetric  expansion  of 
solids  —  expansion  of  liquids  —  maximum  density  of  water  — 
expansion  of  gases  —  the  absolute  scale  —  pressure  coefficient 
of  gases  —  gas  equation  —  hot-air  engine  —  convection  cur- 
rents —  heat  transfer  by  convection  —  heating  and  venti- 
lating systems  —  conduction  —  saving  heat  —  radiation  — 
molecular  theory. 

EXPANSION  BY  HEAT 

162.  Sources  of  heat.  Our  most  important  source  of  heat  is 
the  sun.  The  more  nearly  vertical  the  sun's  rays  are,  the  more 
heat  they  give.  This  explains  why  we  receive  more  heat  at 
noon  than  in  the  morning  or  evening,  more  heat  in  summer 
than  in  winter,  and  more  heat  near  the  equator  than  near  the 
poles. 

The  interior  of  the  earth  is  hot.  Hot  springs  and  volcanoes 
indicate  this.  Also  in  mine  shafts  sunk  into  the  earth  the  tem- 
perature rises  about  one  degree  for  every  hundred  feet  of  depth. 

To  warm  our  houses  and  run  our  engines,  we  do  not  as  yet 
depend  directly  on  the  sun  or  on  the  internal  heat  of  the  earth, 
but  on  the  heat  produced  in  burning  wood,  coal,  oil,  or  gas. 
The  heat  thus  obtained  comes  indirectly  from  the  sun,  having 
been  stored  as  chemical  energy  in  plants  in  past  ages. 

Electricity  is  coming  to  be  more  and  more  a  convenient 
source  of  heat  which  can  be  localized  at  any  desired  point,  as 
in  an  electric  soldering  iron,  a  toaster,  a  flatiron,  or  an  electric 
range.  Electric  ovens  are  used  to  bake  the  enamel  paint  on 
machinery,  and  electric  furnaces  to  prepare  and  refine  metals. 

194 


THE   THERMOMETER 


195 


We  shall  discuss   the    heating  effect   of   electric  currents  in 
Chapter  XVI. 

We  have  already  learned  in  our  study  of  machines  and  in 
our  everyday  experience  that  friction  produces  heat.  For  ex- 
ample, in  scratching  a  match, 
in  using  drills,  saws,  and  files, 
indeed,  whenever  mechanical 
energy  is  apparently  lost,  we 
find  that  heat  appears. 

John  Tyndall  (1820-1893) 
in  his  lectures  on  "  Heat 
considered  as  a  mode  of 


motion 


as    a 
used  to  perform  a 


Striking  experiment   to  show     Fig.  193.     Friction  on  the  rotating  tube 

that  friction  produces  heat.  boas  the  water  within 

Let  us  try  the  same  experiment  by  putting  a  little  water  in  a  metal 
tube  (Fig.  193).  If  we  close  the  tube  with  a  stopper  and  rotate  it 
with  a  motor,  we  find  that  the  friction  between  the  rotating  tube 
and  a  wooden  clamp  generates  in  a  few  minutes  enough  heat  to  boil 
the  water  and  blow  the  stopper  out. 

163.  The  thermometer.     A  deep  cellar  seems  cold  in  summer 
and  warm  in  winter,  even  though  it  remains  at  nearly  the  same 
temperature.     A  room  often  seems  hot  after  we  have  been  out  in 
the  cold,  although  it  seems  chilly  after  we  have  been  in  it  awhile. 
Our  sensations  about  the  temperatures  of  things  are-  therefore 
very  unreliable  and  depend  on  our  own  condition  at  the  moment. 
So  it  is  necessary  to  have  some  kind  of  instrument  to  indicate 
accurately  how  hot  or  cold  things  are;  that  is,  a  thermometer. 
The  usual  form  of  thermometer  is  based  on  the  fact  that  most 
liquids,  such  as  mercury  and  alcohol,  expand  when  being  heated 
and  contract  again  on  cooling. 

164.  Making  a  mercury  thermometer.     A   spherical   or   cylindrical 
bulb  is  blown  on  one  end  of  a  piece  of  glass  tubing  with  a  very  fine 
uniform  bore,  and  the  bulb  and  part  of  the  stem  are  filled  with  mercury. 
When  the  mercury  is  warmed,  it  expands  and  rises  in  the  stem  until 


196        HEAT  —  EXPANSION  AND   TRANSMISSION 


100" 


it  overflows.  Then  the  top  of  the  tube  is  closed  by  melting  the  glass. 
When  the  mercury  cools  again,  it  leaves  a  vacuum  in  the  top  of  the 
tube.  If  the  bulb  is  now  placed  in  the  steam  from  boiling  water, 
the  mercury  rises  to  a  definite  point  on  the  stem,  which  is  marked  with 
a  scratch.  This  point  is  called  the  boiling  point.  If  the  thermometer 
is  then  put  in  melting  ice,  the  mercury  goes  back  down  the  stem  and 
stops  at  a  definite  point.  This  point  is  called  the  freezing  point. 

165.  Centigrade  and  Fahrenheit  scales.  In 
thermometers  that  are  used  for  scientific  work 
the  distance  on  the  stem  between  these  two 

-212*  fjxe(j  points  is  divided  into  100  equal  spaces, 
called  degrees  (Fig.  194) .  In  this  thermometer, 
which  is  called  a  centigrade  thermometer,  the 
freezing  point  is  marked  zero  and  the  boiling 

|  point  is  marked  one  hundred.  When  the  divi- 
sions extend  below  the  zero  point,  they  are 
called  degrees  below  zero,  or  minus  degrees. 

Among  English-speaking  people  a  scale  de- 
vised by  Fahrenheit  in  1714  is  in  common 

w°  use.  On  this  scale  the  freezing  point  is  marked 
32  degrees  (32°)  and  the  boiling  point  212°,  so 
that  the  portion  between  the  freezing  and 
boiling  points  is  divided  into  180  equal  spaces 
(Fig.  194).  Since  100  divisions  on  the  centi- 
grade scale  are  equivalent  to  180  divisions  on 
the  Fahrenheit  scale,  one  division  centigrade 
Fig.  194.  Scales  of  is  equivalent  to  ^  divisions  Fahrenheit.  To 

centigrade      and      ,  ,  ,, 

Fahrenheit  ther-  change  a  temperature  expressed  on  the  centi- 
mometers.  grade    scale    to    the    Fahrenheit    scale,    we 

have  to   remember  that  0°F.  is  32  Fahrenheit  degrees  below 

0°C. 

FOR  EXAMPLE,  68°  F.  is  68-32,  or  36  Fahrenheit  degrees  above  the 
freezing  point ;  and  36  Fahrenheit  degrees  are  equivalent  to  -J  X  36, 
or  20  centigrade  degrees.  Since  the  freezing  point  is  0°  C.,  then  20 
centigrade  degrees  above  this  point  is  20°  C.  Therefore  68°  F.  is 
equivalent  to  20°  C. 


SPECIAL    THERMOMETERS 


197 


To  change  a  Fahrenheit  reading  to  centigrade,  or  vice  versa, 
we  may  use  the  equation : 

|(F-32)  =  C. 

Inasmuch  as  mercury  freezes  at  -39°  C.,  the  thermometers 
used  for  very  low  temperatures  contain  alcohol,  which  is  usually 
colored  red  or  blue. 


166.  Special  thermometers.  Thermometers  are 
made  in  many  special  shapes  and  with  special  pro- 
tecting cases  for  specific  purposes,  such  as  bath  ther- 
mometers, milk  thermometers,  incubator  thermome- 
ters, thermometers  for  candy  making,  thermometers 
to  screw  into  the  sides  of  heaters  or  steam  pipes,  and 
thermometers  specially  designed  for  scientific  work. 
None  of  these  thermometers  differ  in  principle  from 
each  other. 

One  type,  however,  of  great  importance  in  the 
household,  is  made  with  a  special  device  that  everyone 
should  understand.  In  the  clinical  thermometer  (Fig. 
195),  which  is  put  under  the  tongue  of  a  sick  person 
to  detect  fever,  there  is  a  little  constriction  in  the 
bore  of  the  mercury  tube  just  above  the  bulb.  When 
the  mercury  expands,  it  crowds  past  this  constriction 
and  rises  in  the  stem  in  the  usual  way.  When  the 
thermometer  is  taken  out  of  the  patient's  mouth 
to  be  read  and  cools  off  again,  the  mercury  column 
breaks  at  the  constriction  instead  of  running  back 
down  the  stem,  and  continues  to  indicate  the  max- 
imum temperature  reached. 


or         clinical, 
thermometer. 


QUESTIONS  AND  PROBLEMS 

1.  Change  to  centigrade:  70°  F.,  150°  F.,  0°  F.,  -10°  F. 

2.  Change  to  Fahrenheit:  15°  C.,  500°  C.,  -26°  C.,  -190°  C. 

3.  What  would  a  rise  in  temperature  of  80°  on  the  centigrade 
scale  be  in  Fahrenheit  divisions? 

4.  The  temperature  of  the  air  on  a  certain  day  was  90°  F.  at  noon 
and  45°  F.  late  the  next  night.     What  was  the  "  drop  "  in  centigrade 
degrees  ? 


198        HEAT  —  EXPANSION  AND    TRANSMISSION 


5.  At  what  temperature  do  a  centigrade  and  a  Fahrenheit  ther- 
mometer read  the  same? 

6.  How  do  primitive  people  start  a  fire? 

7.  Why  do  sparks  fly  from  car  wheels  when  the  brakes  are  quickly 
applied  ? 

8.  Why  must  a  tool  be  kept  wet  with  cold  water  when  being  sharp- 
ened on  a  grindstone? 

9.  If  one  wants  the  division  marks  far  apart  on  the  stem  of  a 
thermometer,  what  must  be  the  relative  size  of  bulb  and  stem? 

10.  Every  clinical  thermometer  should  be  washed  carefully  before 
and  after  using.     Should  hot  or  cold  water  be  used  ?     Why  ? 

11.  How  is  the  mercury  column  of  a  clinical  thermometer  brought 
down  again  after  it  has  been  read? 

PRACTICAL  EXERCISES 

1.  Maximum  and  minimum  thermometer.  Explain  the  action 
of  the  "  maximum  and  minimum  "  thermometer 
illustrated  in  figure  196.  For  what  would  such  a 
thermometer  be  used? 

2.  Temperature  of  the  body.  After  violent 
physical  exercise  one  feels  very  hot.  Is  the  body 
temperature  higher  than  normal?  Try  it. 

167.  Expansion  by  heat  —  solids.  When 
a  railroad  track  is  built,  gaps  are  usually  left 
between  the  ends  of  the  rails,  to  allow  for  the 
expansion  of  the  steel  in  summer.  Iron  rims 
are  placed  on  wheels  while  hot,  because  they 
are  then  bigger  and  can  be  easily  slipped  on. 
When  they  cool,  they  contract  and  hold  fast 
to  the  wheel.  An  ordinary  wall  clock  loses 


Fig.  196.    Maxi-  time  in  summer  because  its  pendulum  expands 

mum  and  mini-        ,.,,,  .  i       i  AT 

mum  thermome-  a  little  and  so  swings  more  slowly.     Almost 
*er-  all  solids  expand  more  or  less  when  heated,  but 

this  expansion  is  so  very  small  that  one  must  take  special  pains 

to  see  it. 

WTien  solids  expand  and  contract,  they  may  exert  enormous 

forces.     We  can  show  in  a  striking  way  the  force  exerted  by  the 


UNEQUAL  EXPANSION  OF  METALS  199 

expanding  and  contracting  of  a  metal  bar  in  the  following 
experiment. 

In  the  apparatus  shown  in  figure  197  there  is  a  metal  bar  which 
is  heated  by  a  series  of  little  flames  below.     The  expansion,  although 


Fig.  197.    Force  exerted  by  expansion  and  contraction  of  metal  bar. 

very  slight,  is  magnified  by  the  bent  lever  at  the  end ;  as  the  bar  gets 
hot,  the  pointer  rises. 

To  show  that  large  forces  are  exerted  by  an  expanding  or  a  contract- 
ing body,  we  put  a  steel  rod  through  a  hole  in  the  bar  near  where  the 
pointer  touches  it,  and  adjust  the  nut  at  the  other  end  until  the  rod 
rests  against  the  further  side  of  the  slot  in  the  frame.  If  we  then 
heat  the  metal  bar,  the  steel  rod  suddenly  breaks  and  the  pointer 
is  thrown  violently  up.  Then  we  put  another  steel  rod  through  the 
hole,  adjust  the  nut  to  bring  the  rod  against  the  nearer  side  of  the  slot, 
and  allow  the  bar  to  contract.  The  steel  rod  snaps  again  and  the 
pointer  is  thrown  violently  down. 

168.  Unequal  expansion  of  metals.  Careful  experiments 
show  that  different  metals  expand  at  different  rates.  Thus, 
platinum  expands  less  and  zinc  more  than 
other  common  metals.  If  we  made  a  plat-  ass 
inum  meter  rod  correct  at  0°  C.,  it  would 
be  0.9  millimeters  too  long  at  100°  C. 
Similarly  a  steel  meter  rod  would  be  1.3  pig  I9g.  Effect  of  heat- 
millimeters  too  long,  and  a  zinc  meter  rod  ins  a  compound  metal 
would  be  2.9  millimeters  too  long. 

If  two  different  metal  strips,  such  as  iron  and  brass,  are 
riveted  or  welded  together  (Fig.  198),  forming  a  compound  bar, 
the  bar  when  heated  will  bend  or  curl,  because  of  the  unequal 
expansion  of  the  metals. 


200  HEAT — EXPANSION   AND   TRANSMISSION 

A  compound  bar  of  this  sort  is  the  essential  part  of  most  "  metallic 
thermometers."  A  long  bar  is  coiled  in  a  spiral  and  one  end  is  held 
fast,  the  motion  of  the  other  end  being  magnified  and  transmitted 
to  a  pointer.  In  a  recording  thermometer  (Fig.  199)  a  paper  disk 
is  rotated  once  a  day  or  once  a  week  by 
clockwork,  and  a  continuous  record  of  the 
temperature  is  made  by  a  pen  at  the  end  of 
the  pointer. 

The  motion  of  the  free  end  of  a  com- 
pound bar  can  be  made,  not  merely  to  in- 
dicate, but  to  control,  the  temperature  of 
an  inclosed  space ;  such  a  device  is  called 
a  thermostat. 

In  one  type  of  thermostat,   often  used 
Fig.   199.    Recording   ther-   in  chicken  incubators,   the  compound  bar 
mometer.     The  chart  is   raises  or  lowers  a  light  damper  that  con- 
rotated  by  clockwork.  trolg  the  intake  of  warm  air  from  the  heat_ 

ing  lamp.     In  another  type,  used  to  control  electric  heating,  the 
motion  of  the  free  end  of  the  bar  makes  or  breaks  the  current. 

169.  Measurement  of  expansion.  In  considering  how  much 
a  given  object  —  such  as  a  steel  rail  —  will  expand,  it  is  nec- 
essary to  know  three  things  about  it,  namely,  its  length,  the 
rise  in  temperature,  and  the  rate  of  expansion  of  the  particular 
substance  used. 

FOR  EXAMPLE,  if  we  know  that  a  steel  rail  is  33  feet  long  and  each 
foot  of  it  expands  0.000010  feet  per  degree  centigrade,  we  can  com- 
pute how  much  it  will  expand  from  winter  to  summer,  a  range  of  per- 
haps 50°  C.  The  expansion  is  equal  to  the  expansion  per  degree  for 
one  foot,  multiplied  by  the  length  in  feet  and  by  the  rise  in  tempera- 
ture. That  is, 

Expansion  =  0.000010  X  33  X  50 

=  0.0165  feet  =  0.198  inches. 
In  symbols, 

e  =  kl(t'-t) 
where         e   =  expansion,  or  change  in  length, 

k   =  expansion  per  degree,  per  unit  length, 

/    =  length, 

t'  =  temperature  when  hot, 

t    =  temperature  when  cold. 


MEASUREMENT    OF    EXPANSION 


201 


The  factor  k,  called  the  coefficient  of  linear  expansion,  is 

the  expansion  of  a  unit  length  for  1  degree  rise  in  temperature.  It 
is  a  very  small  fraction,  and  varies  with  different  substances. 
Notice  that  no  matter  in  what  unit  the  length  I  is  expressed, 
the  expansion  e  will  come  out  the  same.  Why?  Usually  k  is 
given  per  degree  centigrade,  but  the  coefficient  for  the  Fahren- 
heit scale  can  be  computed  by  multiplying  by  f .  Why? 

The   coefficients   per   degree   centigrade   of    some   common 
substances  are  given  in  the  following  table : 


Zinc 0.000029 

Lead  ......  0.000029 

Aluminum    ....  0.000023 

Tin 0.000022 

Silver 0.000019 

Brass 0.000019 

Copper 0.000017 


Cast  iron    ....  0.000011 

Steel 0.000010 

Platinum    ....  0.000009 

Glass 0.000009 

Pyrex  glass     .     .     .  0.0000032 
"  Invar  "         (nickel 

steel,  36%  Ni)      .  0.0000009 


170.  Some  illustrations.  In  the  construction  of  a 
steel  bridge  allowance  has  to  be  made  for  the  expan- 
sion of  the  steel.  For  example,  in  the  great  bridge  over 
the  Firth  of  Forth  in  Scotland,  which  is  more  than  a 
mile  and  a  half  long,  the  total  allowance  for  expansion 
is  6  feet.  In  steam  plants  long  pipes  are  provided  with 
sliding  or  "  expansion  "  joints,  unless  the  bends  in  the 
pipe  are  such  as  to  yield  enough  for  the  expansion. 

When  a  lamp  chimney  is  heated,  the  glass  expands. 
If  a  drop  of  water  strikes  it,  the  glass  in  the  immedi- 
ate vicinity  cools  rapidly  and  pulls  away  from  the  rest, 
and  the  chimney  cracks. 

Quartz  is  made  into  objects  that  are  as  clear  as  glass, 
but  have  so  small  a  coefficient  of  expansion  (0.0000005) 
that  a  red-hot  quartz  crucible  may  be  suddenly  thrust 
into  water  without  cracking. 

The  pendulum  rod  of  a  clock  is  often  made  of  dry 
wood,  which  expands  very  little.   It  is,  however,  affected 
by  moisture  ;  so  for  accurate  clocks  some  kind  of  com- 
pensated metallic  pendulum  is  used.   One  form  of  com- 
pensated pendulum  is  that  commonly  seen  in  French  F.     2          Com- 
clocks.     It  consists  of  a  glass  tube  or  tubes  filled  with     pensated  mer- 
mercury  (Fig.  200),  suspended  by  a  steel  rod.     When     cury  pendulum. 


202         HEAT  —  EXPANSION  AND   TRANSMISSION 

the  temperature  goes  up,  the  raising  of  the  center  of  gravity  of  the  mer- 
cury, due  to  its  expansion,  is  equal  to  the  lowering  of  the  whole  res- 
ervoir of  mercury,  due  to  the  expansion  of  the  steel  rod,  so  that  the 
effective  length  of  the  pendulum  remains  constant. 

In  a  watch,  the  balance  wheel  if  uncompensated  will  run  slower  in 
hot  weather  because  the  hairspring  has  less  elasticity  at  a  higher 
temperature,  and  also  because  the  expansion  of  the 
radius  of  the  wheel  carries  the  rim  farther  from  the 
center,  and  so  slows  down  its  rotation.  The  rim  is 
therefore  made  of  two  strips  of  metal,  brass  on  the 
outer  edge  and  steel  on  the  inner,  fastened  with  screws 
as  shown  in  figure  201.  When  the  temperature  rises, 
the  free  ends  of  the  rim  curl  inward,  thus  bringing 
part  of  the  rim  nearer  the  axis.  This  compensates 

Fwheel°of  a  watch**   f  or  tne  exPansion  of  tne  crossbar  and  the  weakening 
of  the  hairspring. 

QUESTIONS  AND  PROBLEMS 

1.  A  brass  meter  bar  is  correct  at  15°  C.     What  will  be  the  error 
at20°C? 

2.  A  steel  rail  33  feet  long  is  found  to  expand  0.275  inches  when 
heated  from   -17°  F.  to  100°  F.      What  is  the  coefficient  of  linear 
expansion  on  the  Fahrenheit  scale,  and  also  on  the  centigrade  scale? 

3.  The  steel  cables  of  Brooklyn  Bridge  are  about  5000  feet  long. 
How  much  do  they  change  in  length  between  a  winter  temperature 
of  -20°  F.  and  a  summer  temperature  of  97°  F.? 

4.  A  steel  shaft  is  heated  to  65°  C.  while  being  shaped  in  a  lathe, 
and  its  diameter  at  that  temperature  is  made   just  5  centimeters. 
What  will  its  diameter  be  at  room  temperature  (15°  C.)  ? 

6.  A  steel  wire,  150  centimeters  long  at   15°  C.,  becomes   151.3 
centimeters  long  when  an  electric  current  is  sent  through  it.     How 
hot  does  it  get  ? 

6.'  A  100-foot  steel  tape  is  standard  length  at  62°  F.     How  many 
inches  too  long  will  it  be  at  100°  F.  ? 

7.  Explain  why  pouring  hot  water  on  the  neck  of  a  bottle  will 
sometimes  loosen  a  glass  stopper. 

8.  A  thick  glass  milk  bottle  is  more  likely  to  crack  when  hot  water 
is  poured  into  it  than  a  thin  glass  flask.     Explain. 

9.  Washington  monument  at  noontime  bends  a  few  hundredths 
of  an  inch.     In  what  direction  does  it  lean?     Explain. 


EXPANSION   OF  LIQUIDS  203 

171.  Cubical  expansion  of  solids.     A  metal  bar  when  heated 
expands,  not  only  in  length,  but  also  in  breadth  and  thickness ; 
in  short,  its  volume  increases.     This  expansion  in  volume  is 
called  cubical  expansion.     Suppose  we  have  a  cube  1  centi- 
meter on  an  edge,  at  a  temperature  of  0°  C.,  and  raise  this  to 
1°  C. ;  each  edge  of  the  cube  will  become  (1  +  k)  centimeters,  k 
being  the  coefficient  of  linear  expansion.     The  original  volume,  1 
cubic  centimeter,  will  become  (1  +  A;)3  cubic  centimeters.    Now 
(1  +  k)3  equals  1  +  3  k  +  3  /c2  +  fc3;  but  since   k  is  a  very 
small  fraction,  the  value  of  3  k2  and  k3  will  be  so  small  that 
they  may  be  neglected  without  appreciable  error.     The  volume 
of  the  cube  is,  then,  1  +  3  k ;  hence  the  volume  expansion  per 
cubic  centimeter  per  degree  is  3  k  cubic  centimeters,  and  the 
coefficient  of  cubical  expansion  is  three  times  the  coefficient  of 
linear  expansion. 

FOR  EXAMPLE,  the  coefficient  of  linear  expansion  of  glass  is  0.000009, 
and  the  coefficient  of  cubical  expansion  is  3  times  0.000009,  or  0.000027. 
A  flask  which  held  just  a  liter  at  0°  C.  would  hold 
1002.7  cubic  centimeters  at  100°  C. 

172.  Expansion  of  liquids.     Let  us  fill  a  small 
round-bottomed  flask  with  water  colored  with  ink  and 
insert  a  stopper  with  a  glass  tube  and  paper  scale  (Fig. 
202).    Then  let  us  put  the  flask  into  a  jar  of  ice  water 
and  mark  on  the  scale  the  position  of  the  liquid  in  the 
tube.     If  we  now  put  the  flask  into  a  basin  of  boiling 
water,  we  note  at  first  a  sudden  drop  of  the  liquid  in 
the  tube  (why?)  and  then  a  rapid  rise.    Evidently 
the  liquid  expands  more  than  the  glass. 

In  general,  it  is  found  that  liquids  expand 
much  more  than  solids.  For  example,  when  a 
liter  of  water  is  heated  from  0°  to  100°  C.,  it  in-  Fig  202  Ex_ 
creases  in  volume  about  43  cubic  centimeters,  pansion  of  a 
whereas  a  block  of  steel  of  the  same  volume  would 
expand  only  3  cubic  centimeters.  Mercury,  and  many  organic 
liquids  such  as  ether,  alcohol,  oils,  and  especially  kerosene  ex- 
pand even  more  than  water. 


204         HEAT  — EXPANSION  AND   TRANSMISSION 


Liquids,  like  solids,  expand  with  almost  irresistible  force 
when  heated,  and  exert  enormous  pressures  if  expansion  is  pre- 
vented by  their  surroundings. 

In  the  case  of  liquids  and  gases,  cubical  expansion  rather  than 

linear  is  always  measured. 
Since,  however,  the  vessel  which 
contains  the  liquid  expands 
as  well  as  the  liquid,  we  ob- 
serve only  the  apparent  expan- 
sion. In  a  mercury  thermom- 
eter the  apparent  expansion  is 
only  about  f  of  the  real  expan- 


sion of  the  mercury. 
The    coefficient     of 


cubical 


5°      10°     15°    20°  C. 

TEMPERATURES.        expansion  is  the  expansion  per 
Fig.  203.    Maximum  density  of  water     unit  volume  for  1    degree  rise 

-|j.  *°r*  * 

in  temperature.     For  example, 

the  coefficient  of  cubical  expansion  of  alcohol  is  0.00104  and  of 
mercury  0.000182. 

173.  Abnormal  behavior  of  water.     We  have  just  seen  that 
solids  and  liquids  expand  as  a  rule  when  heated  ;  water  does  the 
same  except  near  its  freezing  point. 

If  we  fill  a  tall  glass  jar  nearly  full  of  cracked  ice  (Fig.  203)  and  let 
it  stand  for  a  while,  the  temperature  of  the  water  near  the  top  comes  to 
0°  C.  and  remains  so,  while  the  temperature  at  the  bottom  is  about 
4°  C.  Since  the  heaviest  liquid  stays  at  the  bottom,  this  means  that 

water  at  4°  C.  is  denser  than  water  at  0°. 

v 
Very  precise  measurements  show  that  water  is  most  dense  at 

4°  C.     When  water  at  4°  C.  is  either  warmed  or  cooled,  it  expands 
and  becomes  lighter,  as  shown  by  the  curve  in  figure  203. 

This  fact  is  important  in  that  otherwise  the  water  in  lakes  would 
freeze  in  winter,  not  merely  at  the  surface,  but  solidly  from  top  to  bot- 
tom, thus  destroying  all  aquatic  life. 

174.  Expansion  of  gases.     We  may  easily  demonstrate  the  great 
expansion  of  a  gas  when  heated,  with  the  apparatus  shown  in  figure 


r 


EXPANSION    OF    GASES 


205 


204.  Even  the  heat  of  the  hand  on  the  flask  causes  bubbles  of  air 
to  be  expelled  from  the  tube  and  to  rise  through  the  water.  If  the 
heat  of  a  flame  is  applied  to  the  flask,  the  bubbles  rise  rapidly.  If 
after  a  time  the  flame  is  removed  and  the  flask  allowed  to  cool,  water 
rises  into  the  flask  to  take  the  place  of  the 
escaped  air.  From  the  volume  of  water  thus 
drawn  up  into  the  flask,  it  is  evident  that  a 
considerable  fraction  of  the  air  was  expelled 
during  the  expansion. 


Fig.     204.      A  gas  ex- 
pands when  heated. 


The  expansion  of  gases,  such  as  air, 
illuminating  gas,  or  hydrogen,  is  remark- 
able for  two  reasons :  first,  because  it  is 
so  large  (about  nine  times  as  much  as  for 
water),  and  second,  because  it  is  nearly 
the  same  for  all  gases. 

The  coefficient  of  expansion  of  a  gas  can 
be  measured  in  a  rough  way  as  follows.  Suppose  we  have  a  tube  of 
uniform  bore  (Fig.  205)  which  is  closed  at  one  end  and  has  a  little 
pellet  of  mercury  to  separate  the  inclosed  gas  AB 
from  the  atmosphere.  (Dry  air  is  a  good  gas  with 
which  to  experiment.)  If  we  put  the  tube  in  a 
freezing  mixture  at  0°  C.,  the  gas  in  the  tube  will 
contract,  and  we  can  measure  the  length  A  B,  which 
we  shall  assume  to  be  273  millimeters.  If  we  put 
the  tube  in  steam  at  100°  C.,  the  gas  will  expand 
and  we  can  measure  its  length  again.  This  length 
AB'  we  shall  find  to  be  about  373  millimeters. 
From  this  experiment  we  see  that  the  air  expanded 
1  millimeter  for  each  degree  rise  in  temperature 
(the  expansion  of  the  glass  can  be  neglected).  That 
is,  the  gas  expanded  ^-}-^,  or  0.00366  of  its  volume 
at  0°  C.  for  each  degree  rise  in  temperature. 


100  C 


B' 


ojc 


I 


In  general,  different    gases  have    nearly  the 
Fig.  205.    Expan-    same  coefficients  of  expansion,  namely,  ^,  or 

sion   of    a    gas     Q.00366. 
under    constant 

pressure.  1?5    Absolute   temperature   scale.     In  the 

experiment  just  described  we  started  with  an  air  column  273 


206         HEAT — EXPANSION   AND   TRANSMISSION 


CENTIGRADE 


ABSOLUTE 


100 


-252.5 
-273° 


-  -  Boiling  Point  of 1 

Water 


— Room  Temperature 

—  Freezing  Point  of 

Water 


373° 


Boiling  Point  of 

Hydrogen — -— — - 

Absolute  Zero 


20.5° 


millimeters  in  length  at  0°  C. ;  if  we  had  cooled  the  gas  from 
0°  to  —1°  C.,  the  length  AB  would  have  been  shortened  a 
millimeter;  and  if  we  had  cooled  it  to  —10°  C.,  the  length 
of  the  air  column  would  have  become  263  millimeters.  If, 

then,  the  air  column  continued  to 
contract  at  the  same  rate  if  cooled 
indefinitely,  the  volume  of  the  air 
at  —273°  C.  would  become  zero. 
As  a  matter  of  fact,  we  can  never 
get  a  gas  to  so  low  a  temperature 
as  —273°  C.,  because  every  known 
gas  turns  into  a  liquid  before  that 
temperature  is  reached.  The  tem- 
perature —  273°  C.  is,  however,  one 
of  unusual  interest  in  the  study  of 
gases.  It  is  called  the  absolute  zero, 
and  temperatures  measured  from 
this  point  as  zero  are  called  abso- 
lute temperatures.  Absolute  cen- 
tigrade temperatures  may  be  designated  by  the  letter  A. 
Thus,  0°  C.  =  273°  A.,  50°  C.  =  323°  A.,  and  100°  C.  =  373°  A. 
To  change  any  temperature  from  the  centigrade  to  the  absolute 
scale  (Fig.  206),  add  273  degrees.  If  we  represent  tempera- 
tures in  the  centigrade  scale  by  t  and  on  the  absolute  scale  by  T, 
we  have 

T  =  t  +  273. 

176.  The  law  of  Charles.  A  little  more  than  a  hundred 
years  ago  a  Frenchman,  Charles,  studied  the  expansion  of 
gases  and  found  that  all  gases  expand  and  contract  to  the  same 
extent  under  the  same  changes  of  temperature,  provided  there 
is  no  change  in  pressure. 

In  general,  when  the  pressure  is  kept  constant,  the  volume  of 
gas  is  very  nearly  proportional  to  its  absolute  temperature.  This 
is  known  as  the  law  of  Charles. 


Fig.  206.     Centigrade  and  abso- 
lute-temperature scales. 


THE  LAW  OF  CHARLES  207 

This  relation  between  the  volume  and  temperature  of  a  gas 
at  constant  pressure  can  be  very  concisely  expressed  by  the 
equation  : 

V      T 

^=T,  a) 

when  V  and  V  represent  the  volumes  of  a  certain  quantity  of 
gas  at  the  same  pressure  but  at  different  absolute  temperatures, 
T  and  Tr. 

From  the  above  discussion  of  absolute  temperature  it  will 
be  seen  that  the  volume  of  any  gas  is  doubled  when  its  tem- 
perature is  raised  from  273°  A.  (0°  C.)  to  2  X  273°,  or  546°  A. 
(273°  C.). 

FOR  EXAMPLE,  suppose  we  have  a  quantity  of  gas  which  occupies 
320  cubic  centimeters  when  the  temperature  is  15°  C.  What  volume 
will  it  occupy  at  0°  C.? 

First  change  the  centigrade  temperatures  given  in  the  problem  to 
absolute  temperatures  by  adding  273  ;  then 

V  _       273 
320     273  -4-  15 


In  solving  such  problems  it  is  advisable  to  compare  the  result 
obtained  by  computation  with  the  original  volume  to  see 
whether  it  is  reasonable.  Thus,  if  the  gas  is  measured  under 
laboratory  conditions  when  the  temperature  is  20°  C.,  the 
volume  of  the  gas  under  standard  conditions  (0°  C.)  would  be 
about  7  per  cent  less. 

PROBLEMS 

1.  What  volume  would  160  cubic  centimeters  of  hydrogen,  meas- 
ured at  17°  C.,  occupy  at  0°  C.? 

2.  If  250  cubic  feet  of  illuminating  gas  were  measured  at  -10°  C., 
what  would  the  volume  be  at  20°  C.  ? 

3.  The  weight  of  22.4  liters  of  oxygen  at  0°  C.  is  32.0  grams.     What 
would  be  the  volume  of  the  same  quantity  of  oxygen  at  25°  C.  ? 


208         HEAT  —  EXPANSION  AND   TRANSMISSION 

4.  At  what  temperature  would  the  volume  of  a  given  quantity 
of  gas  be  exactly  twice  what  it  is  at  17°  C.,  the  pressure  remaining  con- 
stant? 

5.  A  liter  of  air  at  0°  C.  and  atmospheric  pressure  weighs   1.293 
grams.     What  is  the  density  of  air  at  100°  C.  and  atmospheric  pres- 
sure? 

6.  The  coefficient  of  expansion  of  gasoline   is   about   0.0006   per 
degree  Fahrenheit.     If  a  tank  car  contains  100,000  gallons  of  gasoline 
at  60°  F.,  how  much  shrinkage  in  volume  will  occur  when  the  tempera- 
ture drops  to  0°  F.  ? 

177.  Pressure  coefficient  of  gases.  Since  the  volume  of  a 
gas  increases  as  the  temperature  rises,  it  is  reasonable  to  expect 
that  if  a  certain  quantity  of  gas  were  heated  and  yet  confined 
in  the  same  space,  the  pressure  would  increase.  Very  careful 
experiments  have  been  carried  out  to  determine  the  pressure 
coefficient  of  a  gas,  and  the  results  show  that  the  pressure  of 
a  gas  kept  at  constant  volume  increases  for  each  degree  centigrade 
very  nearly  ^,  or  0.00366  of  the  pressure  at  0°  C.,  no  matter  what 
the  gas  is.  It  will  be  noticed  that  this  is  the  same  fraction 
which  we  found  for  the  increase  of  volume  at  constant  pressure. 

It  will  be  more  convenient  to  state  this  in  terms  of  absolute 
temperature,  thus  :  for  all  gases  at  constant  volume,  the  pressure 
is  proportional  to  the  absolute  temperature,  or 


FOR  EXAMPLE,  an  automobile  tire  is  pumped  up  to  a  pressure  of 
70  pounds  per  square  inch  when  the  air  is  at  17°  C.  After  driving 
the  car  on  a  hot  day,  the  temperature  of  the  air  in  the  tube  is  57°  C. 
What  will  the  pressure  become  if  we  assume  that  the  tube  does  not 
stretch? 

70  273  +  17 
P'  273  +  57 
330  X  70 


P'  = 


290 
=  79.8  Ibs.  per  sq.  in. 


THE  GAS  EQUATION  209 

178.  The  gas  equation.  The  relation  between  the  volume 
and  pressure  of  a  gas  at  constant  temperature  may  be  con- 
cisely expressed  by  Boyle's  law  (section  102)  thus  : 

PV  =  P'V'  (III) 

where  V  is  the  volume  of  a  given  quantity  of  gas  under  pressure 
P,  and  V  is  the  volume  of  the  same  gas  under  a  pressure  P', 
the  temperature  in  the  two  cases  being  the  same. 

The  relation  of  the  volume  to  both  pressure  and  temperature 
can  be  expressed  by  the  gas  equation, 

py  ^p'V 
T         T' 

It  will  readily  be  seen  that  this  equation  reduces  to  equation 
III  (Boyle's  law)  when  T  =  T',  and  that  if  V  =  V  the 
equation  becomes  P/T  =  P'/T',  which  is  another  form  of 
equation  II,  and  that  if  P  =  P'  the  equation  becomes  V/T  = 
V'/T',  which  is  another  form  of  equation  I  (Charles'  law). 

FOR  EXAMPLE,  suppose  we  wish  to   find   the  volume  of  a  certain 
quantity  of  gas  under  standard  conditions,  that  is,  at  0°  C.  and  760 
millimeters  pressure,  when  it  is  known  to  occupy   1200  cubic  centi- 
meters at  15°  C.  and  under  a  pressure  of  740  millimeters. 
We  have 

1200  X  740  =   V  X  760 
273  +15    "    273+0 

V' 


QUESTIONS  AND  PROBLEMS 

1.  A  steel  tank  full  of  air  at  15°  C.  under  atmospheric  pressure  was 
sealed  and  thrust  into  a  furnace,  where  it  was  heated  to  1000°  C.    How 
many  atmospheres  of  pressure  did  the  air  then  exert?     Neglect  the 
thermal  expansion  of  the  steel. 

2.  The  pressure  in  the  cylinder  of  an  automobile  engine  just  before 
the  explosion  may  be  5  atmospheres  absolute  ;   after  the  explosion  it 
may  be  12  atmospheres  absolute.     If  the  explosion  be  thought  of  as 
an  instantaneous  warming  of  the  gas  in  the  cylinder,  and  if  the  tem- 
perature beforehand  is  200°  C.,  what  is  the  temperature  after  the 
explosion? 


210         HEAT  — EXPANSION  AND   TRANSMISSION 

3.  A  student  in  a  chemical  laboratory  generates  50  liters  of  hydro- 
gen at  10°  C.,  and  at  a  pressure  of  700  millimeters.     Find  the  volume 
of  the  gas  under  standard  conditions ;  that  is,  at  0°  C.  and  at  760  milli- 
meters. 

4.  At  the  beginning  of  the  so-called  "  compression  stroke  "  in  an 
automobile  engine,  its  cylinder  contains  42  cubic  inches  of  gas  and  air 
at  atmospheric  pressure,  and  at  a  temperature  of  40°  C.     At  the  end 
of  the  compression  the  volume  is  12  cubic  inches  and  the  pressure  is 
5.5  atmospheres.     What  is  the  temperature  ? 

6.  At  sea  level  the  barometer  stands  at  76  centimeters  and  the 
temperature  is  17°  C.,  and  on  a  mountain  top  the  barometer  stands  at 
40  centimeters  and  the  temperature  is  —13°  C.  Compare  the  quan- 
tities of  ah*  in  a  cubic  meter  at  the  two  places. 

6.  A  liter  flask  contains  1.293  grams  of  air  at  0°  C.  and  76  centi- 
meters pressure.  How  many  grams  of  air  will  it  contain  at  50°  C. 
and  50  centimeters  pressure? 

179.  Low  and  high  temperatures.  The  investigations  of 
Lord  Kelvin  and  of  other  scientific  men  all  point  to  the  con- 
clusion that  the  temperature  —273°  C.  is  really  an  absolute 
zero  in  the  sense  that  it  is  the  lowest  possible  temperature  in 
the  universe.  Although  no  one  has  as  yet  succeeded  in  cooling 
a  body  to  absolute  zero,  temperatures  within  a  very  few  degrees 
of  this  point  have  been  attained  by  the  evaporation  of  liquefied 
gases.  With  liquid  air,  temperatures  as  low  as  —200°  C.  may 
be  obtained,  and  with  liquid  hydrogen  —258°  C.  Professor 
Onnes,  at  the  University  of  Leyden  in  Holland,  has  found  that 
the  boiling  point  of  liquid  helium  is  —268.6°  C.,  or  only  about 
4.5°  above  the  absolute  zero ;  and  in  1921  he  cooled  liquid 
helium  to  a  temperature  in  the  immediate  neighborhood  of 
1°  above  the  absolute  zero  by.  boiling  it  at  a  pressure  of  0.02  mm. 
At  these  low  temperatures  rubber  and  steel  become  as  brittle 
as  glass,  and  metals  become  much  better  conductors  of  electricity 
than  at  ordinary  temperatures. 

The  temperatures  which  one  finds  in  the  furnaces  used  to 
melt  metals  are  much  higher  than  the  temperature  of  boiling 
water.  For  example,  iron  melts  at  about  1100°  C.,  platinum 


CONVECTION  CURRENTS 


211 


Fig.  207.     Diagram 
of  hot-air  engine. 


at  1755°  C.,  and  tungsten  at  3000°  C.     Very  high  temperatures 

are   commonly   obtained    by    means  of    the 

electric    arc,    which   gives    3700°  C.     It  is 

estimated  that  the  sun's  temperature  may 

be  as  high  as  6000°  C.  and  that  some  of  the 

stars  may  be  at  50,000°  C. 

180.   Hot-air  engine.    An  interesting  application 

of  the  expansion  of  gases  is  the  hot-air  engine. 

Its  operation  can  be  understood  by  studying  figure 

207.     A  loosely  fitting  plunger  A  moves  up  and 

down  and  thus  shifts  the  air  back  and  forth  in  the 

cylinder  C,  which  is  heated  at   the  bottom  and 

kept   cool  at  the  top.     The  working  cylinder  C' 

has  a  nicely  fitting  piston  B. 

When  the  plunger  A  moves 
down,  the  hot  air  below  is 
transferred  to  the  top,  where 
it  is  cooled.  This  makes  it 
contract.  The  piston  B  is  then  forced  down  by 
the  external  pressure  of  the  atmosphere.  As  soon 
as  the  piston  B  is  near  the  bottom  of  its  stroke, 
the  plunger  A  is  raised,  causing  the  air  to  flow 
back  under  A,  where  it  is  heated  by  the  fire.  This 
makes  it  expand  and  forces  the  piston  B  up  again, 
and  then  the  cycle  is  repeated.  Hot-air  engines 
are  sometimes  used  for  pumping  water  on  a  small 
scale  at  isolated  places,  for  they  do  not  require 
expert  attendants,  and  they  use  any  kind  of  fuel. 
In  general  they  cannot  compete  with  gas  engines 
on  account  of  their  bulk  and  the  rapid  wearing 
out  of  the  heating  surfaces. 


TRANSMISSION  OF  HEAT 

181.  Convection  currents.  To  make  these 
Fig.  208.  Convection  clear,  let  us  try  two  simple  experiments. 

We  cut  off  the  bottom  of  a  bottle  and  bend  a 

glass  tube  (Fig.  208)  so  that  the  ends  can  be  slipped  through  a  stopper 
which  fits  the  neck  of  the  bottle.  If  we  invert  the  bottle  and  fill  it 
with  water  containing  a  little  sawdust,  we  can  see  a  circulation  of  the 


212 


HEAT — EXPANSION   AND    TRANSMISSION 


water  when  a  flame  is  waved  back  and 
forth  from  A  to  B.  We  note  that  the 
direction  is  from  A  to  B.  Why? 

A  box  (Fig.  209)  has  a  glass  front 
and  two  holes  in  the  top  which  are 
covered  with  glass  chimneys.  If  we  put 
a  candle  under  one  chimney,  convection 
currents  of  air  go  down  the  cool  chim- 
ney A  and  up  the  warm  one  B.  A  bit  of 
lighted  touch  paper  held  near  the  top  of 
the  cool  chimney  makes  the  convection 

currents  more  evident. 
Fig.  209.     Convection  current 

All  systems  of  heating  and  ventila- 
tion depend  upon  what  are  called  convection  currents,  which  in 
turn  depend  upon  the  expansion  of  liquids  and  gases.  The 
explanation  of  the  movement  of  convection  currents  is  that  any 
gas  or  liquid  expands  when  heated,  so  that  a  given  quantity  of 
fluid  increases  in  volume  and  consequently  decreases  in  density. 
In  a  convection  current,  the  lighter  fluid  is  pushed  up  by  the 
heavier  surrounding  fluid,  just  as  a  block  of  wood  under  water 
is  pushed  up  by  the  surrounding  water. 


182.  Heat  transfer  by  convection. 

of  a  convection  current  is  warmer 
than  the  returning  part,  there  is  a 
transfer  of  heat  from  the  flame,  or 
other  source  of  heat  at  the  bottom, 
to  the  cooler  parts  of  the  circuit  at 
the  top.  This  process  of  trans- 
porting heat  by  carrying  hot  bodies 
or  hot  portions  of  a  fluid  from  one 
place  to  another  is  called  convec- 
tion. 


Since  the  up-going  part 


Fig.    210.      Convection  currents 
of  air  in  a  room. 


The  heating  of  a  room  by  a  radiator  (Fig.  210)  is  an  example  of  a 
useful  convection  current.  The  warm  air  in  contact  with  the  radiator 
rises,  while  the  cooler  air  in  other  parts  of  the  room  flows  in  along  the 
floor  to  take  its  place. 


DRAFT  IN  A   CHIMNEY 


213 


183.    Draft  in  a  chimney.     To  make  anything  burn,  we  must  fur- 
nish a  continuous  supply  of  fresh  air.     For  example,  in  a  central-draft 
lamp  (Fig.  211)  there  are  holes  in  the  base  so  that  a  current  of  fresh 
air  can  pass  upward  through  the  tube  to  supply 
the  inside  of  the  flame,  and  there  are  holes 
through   the  sides  and  bottom  of  the  burner 
to  supply  fresh  air  to  the  outside  of  the  flame. 
These  currents  are  maintained  by  convection. 
The   air   inside   the    lamp    chimney    becomes 
warmer  and  therefore  less  dense  than  the  out- 
side air,  and  is  pushed  up  by  the  entering  fresh 
ah*. 

The  draft  in  the  chimney  of  a  stove  (Fig.  212) 
or  a  furnace  is  another  example  of  a  convection 
current.  The  hot  gaseous  products  of  the  fire 
are  pushed  up  the  chimney  by  the  cold  heavier 
air  which  enters  under  the  fire.  The  draft  is 
not  so  strong  when  the  fire  is  first  lighted  in  a 
stove  because  the  air  in  the  chimney  has  not 
yet  been  heated.  A  strong  draft  is  obtained  by 
making  a  chimney  as  straight  and  smooth  as 
possible  ;  by  extending  it  above  other  portions 
of  the  building;  by  keeping  it  away  from  an 
outside  wall  where  it  would  cool  off  readily; 
and  by  making  it  double-walled,  so  as  to  keep 
the  chimney  gases  warm  all  the  way  up.  A 
be  so  large  that  the  hot 
neither  must  it  be  so  small 

as     to    impede 

,  ,    .    ,, 

their  flow.    The 

chimneys  used  by  factories 
are  often  very  tall  because  the 
draft  is  due  to  the  difference 
in  total  weight  between  the 
column  of  heated  air  and  a 
similar  cojumn  of  outside 
air,  and  this  difference  is 
nearly  proportional  to  the 
height  of  the  chimney. 

A  great  deal  of  heat  is  car- 
ried  off  by  the  hot  gases  in  a 
chimney,  but  it  must  not  be 


chimney  must  not 
gases  cannot  fill  it  ; 


Fig-  211.    Air  currents  in 

"*  ?bottt  a  central~ 
draft  lamp. 


Fig.  212. 


Circulation  of  hot  gases  about  the 
oven  in  a  kitchen  stove. 


214 


HEAT — EXPANSION  AND   TRANSMISSION 


Overflow  and  air  pipe  running 
to  some  tank  or  drain 


supposed  that  this  heat  is  all  wasted. 
Devices,  called  economizers,  have  been  in- 
vented to  utilize  this  heat  and  to  send 
comparatively  cool  gases  up  the  chimney ; 
but  in  such  cases  huge  power-driven  fans 
have  to  be  used  to  produce  the  required 
draft.  So  we  can  say  that  the  heat  lost  up 
a  chimney  is  the  price  paid  for  the  draft. 

184.  Hot-water  heating.  The 
arrangement  for  heating  water  in  the 
kitchen  boiler  for  general  use  in  laundry 
and  bathroom  is  shown  in  figure  213. 
The  cold  water  enters  the  tank  through 
a  pipe  which  reaches  nearly  to  the 
bottom.  Water  from  the  bottom  of 
the  tank  is  led  to  a  coil  of  pipe  heated 

Fig.  213.    Kitchen  boiler  for  by  a  gas  flame  or  by  the  fire  in  the 
heating  water.  kitchen 

range.  When  this  water  be- 
comes hot,  it  is  pushed  up  and 
goes  back  into  the  tank  at  a 
point  nearer  the  top.  Thus  a 
circulation  is  set  up  which  con- 
tinues until  practically  all  the 
water  in  the  tank  has  passed 
through  the  heating  coil  and  the 
whole  tankful  is  hot. 

The  hot-water  system  of 
heating  houses  (Fig.  214)  de- 
pends on  this  same  principle  of 
convection.  Water  is  heated 
nearly  to  the  boiling  point  in  a 
furnace  in  the  basement.  The 
hot  water  is  led  from  the  top 
of  the  furnace  through  pipes  to 
iron  radiators  in  the  various 


Return  taking 
water  back  from 
other  Radiators 


Fig.  214. 


Hot-water  system  of  heating 
houses. 


HEATING  AND  VENTILATING 


215 


Fig.  215. 


Hot-air  furnace   with  re- 
turn flue. 


rooms  of  the  building.     On  account  of  the  large  exposed  sur- 
face in  each  radiator,  heat  is  rapidly  given  out  by  the  hot  water 
to  the  surrounding  air.     The  cooled  water  is  then  carried  from 
the   radiators    through    return 
pipes  to  the  base  of  the  furnace. 
To  prevent  radiation  from  the 
pipes,    a   thick  non-conducting 
coating  of  asbestos  is  often  pro- 
vided. 

185.  Hot-air  system  of  heat- 
ing and  ventilating.  The  hot- 
air  furnace  in  the  basement 
(Fig.  215)  is  simply  a  big  stove, 
surrounded  by  a  shell  or  jacket 
of  galvanized  sheet  iron.  The 
air  between  the  stove  and  outer 
shell  is  heated  and  is  then  pushed 
up  into  the  flues  by  the  heavier  cold  air  which  comes  in  from  out 
of  doors  through  the  cold-air  inlet  flue.  The  smoke,  of  course, 
goes  up  the  chimney.  Some  of  the  warm  air  which  enters  the 
rooms  escapes  around  the  doors  and  windows ;  the  rest  is 
carried  back  to  the  base  of  the  furnace  by  a  return  flue. 

In  the  hot- water  system  of  heating  there  is  no  provision  what- 
ever for  changing  the  air  in  the  room ;  that  is,  for  ventilation. 
In  the  hot-air  system  a  small  quantity  of  fresh  air  is  continually 
flowing  into  the  rooms.  This  is  enough  for  a  private  house. 
But  in  schools,  churches,  and  other  public  buildings,  large 
quantities  of  clean,  fresh,  warm  air  need  to  be  continually 
supplied  by  other  means.  For  the  proper  ventilation  of  a  room 
it  is  estimated  that  each  person  in  it  requires  about  50  cubic 
feet  of  fresh  air  every  minute.  In  large  modern  school  buildings 
the  air  is  drawn  in  from  out  of  doors  by  powerful  fans,  filtered 
through  cloth,  warmed  by  passing  around  steam  pipes,  and  then 
distributed  in  ducts  throughout  the  building.  The  vitiated  air 
in  each  room  is  forced  out  through  ducts  near  the  floor.  This 


216 


HEAT— EXPANSION  AND   TRANSMISSION 


indirect  system  of  heating,  while  expensive,  furnishes  excellent 
ventilation. 

QUESTIONS  AND  PROBLEMS 

1.  Why  is  an   expansion  tank  necessary  in  a  hot- water  heating 
system  ? 

2.  Why  is  it  essential  to  keep  the  flues  of  stoves  and  furnaces  clean 
and  free  from  soot  and  ashes? 

3.  Explain  why  opening  the  check  draft  in  the  smoke  pipe  of  a 
stove  slows  up  the  fire. 

4.  Explain 
the  purpose  and 
operation  of  the 
in 

Spark  Pluga 


Upper  Tank 


Fan— 
Tubing  and 


Lower  Tank 


Connection  Pipe 


damper 

kitchen     stove 
(Fig.  212). 

5.  Why     is 
the    air     in     a 
room     changed 
more      quickly 
by    opening    a 
window  at  both 
top  and  bottom 
than   if    either 
half  is   opened 
alone  ? 

6.  If  1  cubic 
foot   of   air   at 

0°  C.  weighs  0.081  pounds,  how  much  will  the  air  in  a  chimney  30  feet 
high  and  1  foot  square  weigh  if  heated  to  260°  C.  ? 

7.  The  chimney  for  a  stove  in  an  ordinary  house  is  30  feet  in  height 
and  9  inches  square.     If  the  average  temperature  of  the  flue  gases 
within  is  260°  C.  and  the  air  outside  is  at  0°  C.,  how  many  times  heavier 
is  a  similar  column  of  outside  air  than  that  within  the  chimney? 

8.  Why  should  all  openings  into  a  chimney  be  closed  except  those 
in  actual  use? 

9.  Figure  216  shows  one  type  of  cooling  system  (thermo-siphon) 
used  for  keeping  automobile  engines  from  becoming  overheated.     Ex- 
plain how  the  principle  of  convection  currents  is  illustrated  here. 


Fig.  216. 


Water-cooling  system  for  keeping  automobile 
engines  cool. 


CONDUCTION  IN  SOLIDS  217 

PRACTICAL  EXERCISE 

Model  of  a  hot-water  heating  system.  Set  up  a  model  of  a  hot- 
water  heating  system.  This  can  be  constructed  from  bottles,  flasks, 
stoppers,  and  tubes  found  in  any  chemical  laboratory.  Demonstrate 
the  operation  of  your  model.  For  further  details  see  Good's  Labora- 
tory Projects  in  Physics  (Macmillan). 

186.  Conduction  in  solids.  Besides  transporting  heat  by 
carrying  hot  bodies  about,  or  by  making  hot  fluids  flow  through 
pipes,  we  can  transmit  heat  without  moving  any  material  thing 
by  either  of  two  methods  called  conduction  and  radiation. 

Everyone  knows  that  the  handle  of  a  silver  spoon  gets  hot 
when  its  bowl  is  in  a 
cup  of  hot  tea  or 
coffee.  If  one  end 
of  an  iron  poker  is 
put  in  the  fire,  the 
other  end,  unless  pro- 
vided with  a  wooden 

handle,    SOOn     burns     Fig'  2I7'     Dative  conductivity  of  copper  and  iron. 

one's  hand.  Yet  if  a  wooden  rod  is  plunged  into  a  fire,  it  is 
hard  to  feel  any  warmth  at  the  other  end.  So.  we  conclude 
that  silver  and  iron  conduct  heat  better  than  wood.  In  gen- 
eral, metals  are  good  conductors  of  heat. 

There  are  some  substances,  such  as  stone,  glass,  wood,  wool, 
fur,  and  ashes,  which  are  poor  conductors  of  heat  and  are  there- 
fore called  heat  insulators.  The  metals,  such  as  silver,  copper, 
brass,  iron,  lead,  etc.,  are  good  conductors  as  compared  with 
the  non-metals.  Careful  study  shows  that  even  the  metals 
vary  in  their  power  to  conduct  heat,  that  is,  in  conductivity. 
This  can  be  shown  by  the  following  experiment. 

Let  us  fasten  with  sealing  wax  a  number  of  steel  balls  at  regular 
intervals  on  the  under  side  of  two  rods,  one  of  copper  and  one  of  iron. 
If  we  heat  one  end  of  each  rod  in  a  flame  (Fig.  217),  the  balls  on  the 
copper  rod  soon  drop  off,  beginning  near  the  flame.  Later  the  balls 
on  the  iron  rod  begin  to  drop  off.  Often  half  the  balls  will  have 
dropped  from  the  copper  rod  before  the  first  one  drops  from  the  iron  rod. 


218 


HEAT — EXPANSION  AND   TRANSMISSION 


Liquids  and  gases 
This  can  be  shown 


Fig.  218.  Water  is  such  a  good 
heat  insulator  that  ice  and  boiling 
water  may  be  in  the  same  test 
tube. 


187.  Conduction  in  liquids  and  gases, 
are  much  poorer  conductors  than  metals, 
by  the  following  experiment. 

Let  us  take  a  large  test  tube  full  of  water  and  place  in  it  a  few  pieces 
of  ice,  which  are  held  near  the  bottom  by  a  wire  grid,  as  shown  in 

figure  218.  Then  we  may  boil  the 
water  at  the  top  of  the  tube  for  some 
time  without  melting  the  ice  in  the 
bottom. 

Experiments  to  measure  con- 
ductivity show  that  iron  conducts 
100  times  as  well  as  water,  and 
that  water  conducts  25  times  as 
well  as  air. 

It  is  an  interesting  fact  that 
substances  which  are  good  con- 
ductors of  heat  are  good  conduc- 
tors of  electricity  as  well. 

188.  Applications.    These  differences  in  conductivity  explain  why 
pokers  and  teapots  have  wooden  or  insulated  handles ;  why  a  vacuum 
bottle  (Fig.  219)  keeps  things  hot  or  cold  a  long  time ;    and  why  we 
wear  woolen  clothing  in  winter.     Woolen  clothing 

of  loose  texture,  furs,  feathers,  and  eiderdown 
quilts  are  effective  as  heat  insulators,  because 
much  air  is  inclosed  in  their  pores  and  yet  convec- 
tion currents  are  prevented. 

Differences  in  conductivity  also  account  for  many 
curious  sensations  of  heat  and  cold.  Thus  in  a 
cool  room  some  things  feel  much  colder  than 
others.  Metallic  objects,  which  are  good  con- 
ductors, take  heat  rapidly  from  the  hand,  and  so 
give  the  sensation  of  cold.  Other  objects  such  as 
wood  and  paper,  carry  off  the  heat  of  the  hand 
slowly  and  so  do  not  feel  cold.  Similarly,  a  piece 
of  metal  lying  in  the  hot  sun  feels  much  warmer 
than  a  piece  of  wood  beside  it. 

189.  Saving  heat.  Since  the  saving  of  heat 
means,  in  general,  the  saving  of  fuel,  the  conservation  of  heat  is 


Fig.  219.  Section  of 
a  vacuum,  or  ther- 
mos, bottle. 


SAVING  HEAT 


219 


a  question  of  national  economy.    Heat  always  tends  to  pass  from 

warmer  objects  to  cooler  ones  and  can  never  be  entirely  retained. 

Nevertheless  a  knowledge  of  the  properties  of  heat  insulators 

makes  it  possible  to  save  much  heat  which  would  otherwise  be 

lost.     For  example,  the  walls  of 

steel    passenger    cars    are   lined 

with  a  layer  of  heat  insulating 

material,  because  the  steel  is  so 

good  a  conductor  of  heat  that 

such  cars  would  waste  too  much 

heat  in  winter.     For  the  same 

reason  the  walls  of  a   house  are 

built  with  an  air  space,  as  shown 

in  figure  220.     Double  windows 

in  winter,  by  forming  a  dead-air 

space,    save   large    amounts    of 

heat.     Better  insulation  around 

a  furnace  or  heater  and  around 

the  pipes  through  which  heat  is 

distributed  to  various  parts  of 

a  house  often  pays  for  itself  in 

a   short    time    by   saving    coal. 

In  industrial  plants  steam  pipes  should  be  well  insulated  with 

asbestos   or   magnesia  for   the   same   reason.     Much   heat   is 

wasted  in  dwellings  by  allowing  currents  of  warmed  air  to  escape 

through  open  fireplaces  ;  dampers  in  the  chimney  throats  above 

fireplaces  should  be  kept  closed  when  the  fireplaces  are  not  in 

use.  In  cold  weather  the  cold-air  intake  duct  of  a  hot-air  furnace 

should  be  kept  nearly  closed,  the  circulation  through  the  furnace 

being  maintained  by  one  or  more  return  flues  frorfi  the  house 

itself. 

Another  important  means  of  saving  heat  is  the  fireless  cooker 
(Fig.  221).  In  this  case  a  compartment,  usually  lined  with 
sheet  metal,  is  so  thickly  covered  on  all  sides  with  some  sort  of 
insulating  material  that  the  contents  once  heated  will  stay  hot 


Fig.  220.     Wall   of    a    frame    house 
showing  air  space. 


220 


HEAT — EXPANSION  AND   TRANSMISSION 


for  many  hours.     A  hot  stone  is  often  placed  under  the  dish  to 
act  as  a  storage  reservoir  of  heat. 

PRACTICAL  EXERCISE 

Making  a  fireless  cooker.  Full  directions  may  be  found  in  Farmers' 
Bulletin  771,  U.  S.  Department  of  Agriculture.  How  would  you  test 
its  efficiency? 

190.  Radiation.  If  an  iron  ball  is  heated  and  hung  up  in 
the  room,  the  heat  can  be  felt  when  the  hand  is  held  under 

the  ball.  This  cannot  be  due  to 
convection,  because  the  hot-air 
currents  would  rise  from  the  ball. 
It  cannot  be  due  to  conduction, 
because  gases  are  very  poor  con- 
ductors. Similarly  a  lighted  elec- 
tric-light bulb  feels  hot  if  the  hand 
is  held  near  it,  but  when  the  light  is 
turned  off,  the  sensation  stops  very 
quickly.  The  glass  of  the  bulb  is 
a  very  poor  conductor  and  there 
is  practically  no  air  left  inside  the 
bulb,  so  that  the  sensation  of  heat 
can  be  due  neither  to  convection 
nor  to  conduction.  Furthermore, 
an  enormous  quantity  of  heat  comes 
to  us  from  the  sun.  Yet  men  who 
make  ascents  in  balloons  and  air- 
planes find  that  the  air  becomes  less  and  less  dense,  so  that  it 
seems  reasonable  to  suppose  that  the  earth's  atmosphere  forms  a 
coating  only  a  few  miles  thick  and  that  the  space  beyond  is 
absolutely  empty.  So  the  sun's  heat  cannot  come  by  convection 
or  conduction. 

To  explain  these  phenomena,  scientists  have  imagined  a 
weightless,  elastic  fluid  called  the  ether  which  fills  all  space  and 
transmits  heat  and  light  by  a  process  called  radiation.  When 
a  body  not  in  contact  with  conducting  bodies  cools,  it  is  said  to 


Fig.  221.     Fkeless  cooker  con- 
serves heat. 


RADIANT  HEAT 


221 


radiate  heat,  or  to  cool  by  radiation.  If  a  screen,  such  as  a 
book,  is  placed  between  a  lighted  lamp  and  one's  face,  the  heat 
is  no  longer  felt.  So  we  think  that  heat  rays,  like  light  rays, 
travel  in  straight  lines.  Experiments  also  show  that  heat  rays, 
like  light  rays,  can  be  reflected  by  a  mirror,  or 
brought  to  a  focus  by  a  burning  glass. 

Some  substances,  such  as  glass  and  air,  let  the 
sun's  heat  rays  pass  through  almost  unimpeded 
and  are  warmed  but  little  by  this  radiant  heat ; 
that  is,  they  are  "  transparent-to-heat."  Other 
substances,  such  as  water,  do  not  let  heat  pass 
through  and  are  warmed  by  any  radiant  heat  Fig.  222.  Radiom- 
rays  that  strike  them ;  they  are  "  opaque-to-  tecting^radiant 

heat."  energy. 

191.   Reflection  and  absorption  of  radiant  heat.     We  may 

detect  radiant  heat,  or  energy,  by  means  of  the  radiometer  (Fig.  222). 
The  glass  bulb  incloses  four  vanes  which  are  coated  with  lampblack  on 
one  side  and  are  bright  on  the  other.  These  are  fastened  to  a  vertical 
axis  so  as  to  rotate  very  easily.  The  air  has  been  nearly  exhausted 
from  the  bulb.  When  radiant  heat  strikes  the  vanes,  they  revolve 
in  such  a  direction  that  the  blackened  surface  is  always  retreating. 
The  velocity  of  rotation  depends  roughly  on  the  energy  received. 


^=^ 


Fig.  223.     Radiant  energy  reflected  by  concave  mirrors. 

We  may  show  the  reflection  of  radiant  energy  by  placing  two  con- 
cave mirrors  as  in  figure  223.  The  iron  ball  is  heated  almost  to  redness, 
and  placed  so  far  from  the  radiometer  that  there  is  no  rotation  due  to 
direct  radiation.  Then  the  mirrors  are  set  so  that  the  ball  and  radiom- 


222         HEAT  —  EXPANSION  AND   TRANSMISSION 

eter  are  in  the  foci  of  their  respective  mirrors.    Now  the  vanes  rotate 
briskly  because  of  the  reflected  energy. 

A  mirror,  or  any  highly  polished  surface,  is  a  good  heat  re- 
flector, and  yet  itself  remains  cold.  Fresh  snow  melts  slowly  in 
the  sun's  rays,  but  snow  covered  with  soot  or  black  dirt  absorbs 
radiant  heat  and  melts  rapidly.  In  general,  reflecting  or  white 
objects  do  not  easily  absorb  radiant  heat,  while  rough  or  black 
objects  absorb  radiant  heat  readily. 

It  has  also  been  found  that  reflecting  and  bright-colored 
objects,  when  hot,  cool  by  radiation  more  slowly  than  rough 
and  dark  objects.  For  example,  a  brightly  polished  silver 
cup  radiates  heat  twenty  times  more  slowly  than  a  sooty  black 
cup.  In  general,  good  absorbers  are  good  radiators,  and  poor 
absorbers  are  poor  radiators. 

Very  sensitive  thermoelectric  detectors  of  radiant  heat  have  recently 
been  developed  to  such  a  degree  of  perfection  as  to  respond  to  the 
radiation  from  a  single  candle  a  mile  away.  They  have  been  used  to 
measure  the  heat  radiated  by  a  single  star  in  the  sky ;  to  locate  hostile 
bombing  airplanes  at  night  by  detecting  and  getting  the  direction  of  the 
heat  radiated  by  their  engines;  and  even  to  give  warning  of  trench 
raids  by  responding  to  the  heat  radiated  by  the  bodies  of  approaching 
soldiers. 

QUESTIONS 

1.  Explain  how  flooding  a  cranberry   bog   helps   to  protect  the 
berries  from  frost. 

2.  Give  two  reasons  for  putting  ashes  on  icy  sidewalks. 

3.  How  does  the  glass  in  a  hot-house  act  as  a  trap  to  catch  heat? 

4.  Why  does  an  aviator  encounter  intense  cold  at  high  altitudes 
although  his  flight  has  brought  him  nearer  to  the  sun? 

6.  Which  is  warmer,  an  observer  on  a  mountain  top,  or  one  in  an 
airplane  at  the  same  level,  but  over  a  low-lying  plain? 

6.  Does  woolen  clothing  supply  any  heat  to  maintain  the  body's 
temperature  ? 

7.  Why  do  people  prefer  to  wear  white  clothes  in  summer  and  in 
hot  countries  ? 


MOLECULAR   THEORY  OF  HEAT  223 

8.  Why  should  the  surface  of  a  teakettle  be  brightly  polished  and 
the  bottom  blackened  ? 

9.  Is  it  advisable  to  put  any  sort  of  aluminum  or  gold  paint  on  a 
radiator  that  is  to  heat  a  room? 

10.  What  does  one  mean  by  speaking  of  the  cold  getting  into  a 
house? 

11.  What  would  be  the  advantage  in  nickel-plating  a  kitchen  stove 
instead  of  giving  it  a  black  finish  ?     What  would  be  the  disadvantage  ? 

192.  Theory  as  to  what  heat  is.  There  are  many  reasons 
for  thinking  that  heat  is  a  rapid  vibratory  motion  of  the  mole- 
cules of  substances  or  of  the  ether  which  fills  the  spaces  between 
the  molecules.  We  imagine  that  the  molecules  in  a  hot  flat  iron 
are  vibrating  more  rapidly  than  when  it  is  cold,  and  that  this 
molecular  vibration  extends  to  the  surrounding  ether  and  so  is 
sent  out  in  straight  lines  in  all  directions  as  radiant  heat. 

At  a  temperature  of  about  550°  C.  iron  becomes  "  red  hot," 
and  at  1300°  C.  it  gets  "  white  hot."  We  imagine  that  the 
iron,  before  it  begins  to  glow,  is  sending  out  dark  heat  rays ; 
but  that,  when  red  hot  or  white  hot,  it  is  sending  out  visible 
heat  rays,  that  is,  light  rays.  We  think  that  these  heat  rays 
and  light  rays  differ  only  in  the  rapidity  of  the  vibratory  motion, 
and  in  their  effect  on  the  eye.  If  the  vibrations  are  under  400 
trillion  per  second,  we  recognize  them  as  heat;  but  if  the  vibra- 
tions are  between  400  and  800  trillion  per  second,  the  nerves 
of  the  eye  recognize  them  as  light.  Heat  and  light  are  both 
forms  of  radiant  energy.  This  radiant  energy  travels  at  the 
enormous  speed  of  187,000  miles  per  second,  which  means  that 
radiant  energy  could  circle  the  earth  seven  times  in  one  second. 

On  this  theory,  the  expansion  of  bodies  when  heated  is  due 
to  the  more  violent  vibration  of  their  molecules,  which  require 
more  room  to  move  about  in.  At  a  certain  temperature  this 
motion  becomes  so  violent  that  the  molecules  break  away  from 
their  former  position  and  the  body  changes  its  state ;  that  is, 
it  melts  or  boils.  At  absolute  zero  this  molecular  motion  be- 
comes nil. 


224         HEAT  —  EXPANSION  AND   TRANSMISSION 
SUMMARY   OF  PRINCIPLES   IN    CHAPTER   X 


100  Centigrade  degrees  =  180  Fahrenheit  degrees. 
Temp.  Cent.  =  |  (Temp.  Fahr.  -  32). 

Coefficient  of  linear  expansion 

=  expansion  per  degree  for  unit  length 

expansion 

length  X  rise  in  temperature 
Expansion  =  coefficient  X  length  X  rise  in  temperature. 

Coefficient  of  volume  expansion 

=  expansion  per  degree  for  unit  volume 

expansion 

volume  X  rise  in  temperature 

Expansion  =  coefficient  X  volume  X  rise  in  temperature. 
For  solids,  volume  coefficient  =  3  X  linear  coefficient. 

~  ~  .         t  pressure  rise 

Pressure  coefficient  of  gases  = 

pressure  X  temperature  rise 

Pressure  rise  =  coefficient  X  pressure  X  temperature  rise. 

Volume  coefficient  of  all  gases  nearly  the  same,    -> 
Pressure  coefficient  of  all  gases  nearly  the  same.  I  Value  •— 
Volume  and  pressure  coefficients  nearly  equal.      J 

PV     P'V 
Gas  law:  — =  —f 

Heat  is  transmitted  by  convection,  conduction,  and  radiation. 
Liquids  and  gases  carry  heat  by  the   motion    of   the  heated 

particles  away  from  the  source  of  heat.     A  convection 

current  is  the  result  of  expansion. 
Liquids  and  gases  are  in  general  poor  conductors. 
Radiation  is  the  process  of  transmitting  energy  by  means   of 

ether  waves.     The  sun  is  the  great  source  of  radiant 

energy.     Rough,  black  bodies  are   the  best  radiators 

and  absorbers. 


QUESTIONS  225 

QUESTIONS 

1.  Is  friction  ever  a  source  of  useful  heat? 

2.  Are  the  sun's  rays  ever  used  practically  as  a  direct  source  of  heat 
for  engines? 

3.  Why  does  spring  water  seem  warm  in  winter  and  cool  in  summer  ? 

4.  Why  does  the  water  seem  much  colder 
before  a  bath  than  afterwards? 

6.   Why  can  a  platinum  wire  be  sealed  or 

melted  into  glass  while  a  copper  wire  cannot? 

,   Fig.  224.     Wire  handle  on 

6.  Why  do  glass  bottles  crack  when  placed  stove  lifter. 

on  a  hot  stove? 

7.  Why  does  a  spiral  wire  handle  on  a  poker  or  lifter  (Fig.  224) 
protect  the  hand  so  much  more  than  a  solid  metal  handle  of  similar 
shape  ? 

8.  Why  is  a  fur  coat  warmer  if  the  fur  is  on  the  inside  than  if  the 
fur  is  on  the  outside? 

9.  Is  there  any  other  reason  than  convenience  for  putting  furnaces 
in  cellars  rather  than  in  attics  ? 

10.  What  keeps  the  water  in  the  hot-water  pipes 
in  a  house  hot? 

11.  Does  a  hot  body  cool  more  rapidly  if  placed 
on  metal  than  if  placed  on  wood  ?     Why  ? 

*12.   Why  does  a  glowing  coal  die  out  quickly  on  a 
metal  shovel,  and  yet  glow  for  a  long  time  in  ashes  ? 

13.  Look  up  Davy's  lamp  (Fig.  225)  for  miners  in 
an  encyclopedia.    What  is  its  advantage?     Why  is  it 
that  a  flame  will  not  strike  through  the  fine-mesh  wire 
gauze  ? 

14.  Why  are  the  walls  of  ice  houses  often  packed 
with  sawdust? 

lgsafety  lamp^  S        ^-    Why  should  an  air  space  be  left  in  building  the 
walls  of  brick  and  cement  houses  ? 

PRACTICAL  EXERCISE 

The  use  of  dampers.  Describe  carefully  with  the  aid  of  a  diagram 
all  the  "  dampers  "  of  some  stove  or  furnace  you  have  seen,  and  explain 
how  they  accomplish  the  desired  results. 


CHAPTER  XI 

WATER,   ICE,  AND   STEAM 

Measurement  of  heat  —  B.t.u.  and  calorie  —  specific  heat 
—  freezing  point  —  change  of  volume  in  freezing  —  heat  of 
fusion  of  ice  —  boiling  point  under  various  pressures  —  distil- 
lation —  heat  of  vaporization  of  water  —  steam  heating  —  hu- 
midity —  fog,  rain,  and  snow  —  ice-making. 

193.  How  we  measure  heat.  If  a  man  buys  a  ton  of  coal, 
what  does  he  get  for  his  money?  One  answer  would  be,  about 
2000  pounds  of  material,  of  which,  perhaps,  60  pounds  is  water, 
240  pounds  is  ash,  and  the  rest  mostly  carbon  and  hydrogen. 
What  the  man  is  really  interested  in,  however,  is  not  the  sort 
of  material,  but  the  amount  of  heat  he  has  bought.  Since  heat 
is  not  a  substance,  but  a  form  of  energy,  we  cannot  measure  it 
directly  in  pounds  or  quarts,  but  must  measure  it  by  the  effect 
it  can  produce.  For  example,  if  one  pound  of  hard  coal  could 
be  completely  burned,  and  if  all  the  heat  generated  in  this 
process  could  be  used  to  heat  water,  it  would  be  found  that 
about  7  tons  of  water  could  be  raised  1°  F.  in  temperature. 
Engineers  reckon  the  heat  value  of  fuel  in  units  such  that  each 
represents  the  heat  required  to  raise  one  pound  of  water  one  degree 
Fahrenheit.  This  heat  unit  is  called  the  "  British  thermal  unit," 
and  is  written  B.t.u. 

Some  average  heat  values  are : 

Illuminating  gas 600  B.t.u.  per  cu.  ft. 

Dry  wood 5000  B.t.u.  per  pound 

Dry  coal 14,000  B.t.u.  per  pound 

Kerosene  or  gasoline 19,000  B.t.u.  per  pound 

The  heat  unit  employed  in  Europe,  and  in  all  physical  and 
chemical  laboratories,  is  a  metric  unit  called  the  gram  calorie. 

226 


SPECIFIC  HEAT  227 

The  gram  calorie  is  the  heat  required  to  raise  the  temperature  of  a 
gram  of  water  one  degree  centigrade. 

194.  Heat  absorbed  by  different  substances.  It  is  well 
known  that  a  kettle  of  water  on  a  stove  gets  warm  much  less 
quickly  than  a  flatiron  of  the  same  weight.  The  heat  which 
is  required  to  warm  a  kilogram  of  water  1  degree  will  warm 
the  same  weight  of  aluminum  about  5  degrees,  of  zinc  or  copper 
about  10  degrees,  of  silver  or  tin  about  20  degrees,  and  of  lead 
or  mercury  about  30  degrees.  In  fact,  experiments  show  that 
water  requires  more  heat  per  unit  weight  per  degree  rise  of  tem- 
perature than  any  other  common  substance. 

Since  one  calorie  is  required  to  raise  the  temperature  of  one 
gram  of  water  1  degree,  only  one  tenth  of  a  calorie  would 
be  needed  to  raise  the  temperature  of  one  gram  of  copper  a 
degree,  one  twentieth  of  a  calorie  to  raise  a  gram  of  silver  1 
degree,  and  one  thirtieth  of  a  calorie  to  raise  a  gram  of  lead  1 
degree.  The  number  of  calories  required  to  raise  the  temperature 
of  a  gram  of  a  substance  one  degree  centigrade  is  called  its 
specific  heat.  Thus  the  specific  heat  of  water  is  1,  of  copper 
about  0.1,  etc.  In  the  English  system  the 
specific  heat  of  a  substance  is  the  number  of 
B.t.u.  required  to  raise  the  temperature  of  a 
pound  of  the  substance  one  degree  Fahrenheit. 
Notice  that  the  numerical  value  of  a  specific 
heat  is  the  same  in  both  systems.  Why? 

The  following  experiment  illustrates  how 
much  substances  differ  in  their  specific  heats. 

We  may  heat  a  number  of  cylinders  of  the  same     Fig.  226.     Metals 
weight  but  of  different  metals,  such  as  iron,  cop-        differ    in   specific 
per,  tin,  and  lead,  to  about  150°  C.  in  oil.     Then        ^ter  ^s^ecific 
if  we  place  them  all  at  the  same  time  on  a  thin  cake        heat  than  lead, 
of  paraffin  wax,  as  shown  in  figure  226,  they  will 
melt  the  wax  and  sink  into  it,  but  to  different  depths.    The  iron  sinks 
farthest,  the  copper  and  tin  come  next,  while  the  lead  makes  but  little 
headway.     The  metal  with  the  largest  specific  heat  gives  out  the  largest 
amount  of  heat  in  cooling,  and  so  melts  the  most  paraffin. 


228  WATER,   ICE,   AND  STEAM 

195.  How  specific  heat  is  determined.  When  a  hot  sub- 
stance, such  as  hot  mercury,  is  poured  into  cold  water,  the 
water  and  mercury  soon  come  to  the  same  temperature.  The 
heat  given  up  by  the  cooling  mercury  is  used  in  warming  the 
water.  If  no  heat  is  lost  in  the  process,  the  heat  units  given  out 
by  the  hot  body  are  equal  to  the  heat  units  gained  by  the  cold  body. 

This  method  of  mixtures  is  accurate  only  when  no  heat  is 
lost  during  the  transfer.  This  is  rather  difficult  to  manage  in 
practice.  Nevertheless,  the  method  is  the  one  generally  used 
in  laboratories  to  determine  the  specific  heats  of  substances. 

FOR  EXAMPLE,  suppose  that  300  grams  of  mercury  are  heated  to 
100°  C.  and  then  quickly  poured  into  100  grams  of  water  at  10°  C., 
and  that,  after  stirring,  the  temperature  of  the  water  and  mercury  is 
18.2°  C. 

If  we  let  x  be  the  specific  heat  of  the  mercury,  the  mercury  gives  out 
300(100  -  18.2)x  calories.  Since  the  specific  heat  of  water  is  1,  the 
water  absorbs  100(18.2  —  10)1  calories.  Therefore  we  may  make  the 
equation 

Heat  given  out  =  Heat  taken  in. 
300(100  -  18.2)x  =  100(18.2  -  10)1 
whence  x  =  0.033  calories. 

By  very  careful  experiments  of  this  sort  the  specific  heats 
of  some  of  the  common  substances  have  been  found  to  be  as 
follows : 

TABLE  OF  SPECIFIC  HEATS 
(Either  metric  or  English  units) 


Water 1.00 

Ice 0.50 

Air    .     .     . 0.24 

Aluminum 0.22 

Dry  soil 0.20 

Iron  .  .  0.11 


Zinc 0.094 

Copper     .......  0.093 

Silver  .     . 0.056 

Tin 0.055 

Mercury 0.033 

Lead    .  .  0.031 


It  is  remarkable  that  of  all  ordinary  substances  water  has 
the  greatest  specific  heat.  Thus  it  takes  about  five  times  as 
much  heat  to  raise  a  pound  of  water  1  degree  as  to  raise  a 
pound  of  solid  earth  1  degree,  and  so  the  ocean  acts  as  a  great 


PROBLEMS  229 

moderator  of  temperatures.  In  summer  the  water  absorbs  a 
vast  amount  of  heat,  which  it  gives  up  slowly  in  winter  to  the 
land  and  air.  This  explains  why  the  temperature  on  some  ocean 
islands  does  not  vary  more  than  10°  F.  during  the  whole  year. 

PROBLEMS 

1.  How  many  calories  of  heat  are  needed  to  raise  the  temperature 
of  10  grams  of  water  5°  C.  ? 

2.  How  many  calories  are  required  to  heat  15  grams  of  iron  20°  C.  ? 

3.  Compute  the  calories  given  out  by  a  kilogram  of  copper  in  cool- 
ing from  110°  C.  to  15°  C. 

4.  How  many  B.t.u.  are  necessary  to  heat  a  2-pound  flatiron  from 
70°  F.  to  350°  F.? 

6.    From  the  definition  of  the  two  units  of  heat,  compute  the  num- 
ber of  calories  which  are  equivalent  to  1  B.t.u. 

6.  How  many  tons  of  water  can  be  heated  from  32°  to  212°  F.  by 
the  combustion  of  1  ton  of  coal,  in  a  boiler  whose  efficiency  is  75  %  ? 

7.  If  coal  costs  $5.00  per  ton  and  gas  costs  $1.00  per  1000  cubic 
feet,  how  much  heat  (B.t.u.)  can  be  secured  for  1  cent's  worth  of  each? 

8.  How  much  does  it  cost  to  heat  30  gallons  of  water  from  50°  F. 
to  200°  F.  with  a  gas  heater  whose  thermal  efficiency  is  75%? 

9.  If  400  grams  of  water  at  100°  C.  are  mixed  with  100  grams  of 
water  at  20°  C.,  what  will  be  the  temperature  of  the  mixture? 

10.  It  is  desirable  to  prepare  a  bath  containing  20  gallons  of  water 
at  40°  C.     If  the  supply  of  hot  water  is  at  60°  C.  and  that  of  cold 
water  at  10°  C.,  how  much  of  each  would  you  use? 

11.  If  500  grams  of  copper  at  100°  C.,  when  plunged  into  300  grams 
of  water  at  10°  C.,  raise  the  temperature  to  22°  C.,  what  is  the  specific 
heat  of  copper? 

12.  A  piece  of  iron  weighing  150  grams  is  warmed  1°  C.     How  many 
grams  of  water  could  be  warmed  1°  by  the  same  amount  of  heat  ?     (The 
answer  is  called  the  water  equivalent  of  the  piece  of  iron.) 

13.  A  50-pound  iron  ball  is  to  be  cooled  from  1000°  F.  to  80°  F.  by 
putting  it  in  a  tank  of  water  at  32°  F.     How  many  pounds  of  water 
must  there  be  in  the  tank  ? 

14.  A  platinum  ball  weighing  100  grams  is  heated  in  a  furnace  for 
some  time,  and  then  dropped  into  400  grams  of  water  at  0°  C.,  which  is 
raised  to  10°  C.     How  hot  was  the  furnace?     (Sp.  heat  =  0.04.) 


230  WATER,   ICE,   AND  STEAM 

15.  A  copper  kettle  weighing  1000  grams  contains  2000  grams  of 
water  at  10°  C.     Heat  is  supplied  by  a  gas  flame  which  furnishes 
15,000  calories  per  minute.     How  long  a  time  will  be  required  to  raise 
the  water  to  100°  C.  ? 

16.  When  a  hot-air  furnace  is  driven  on  a  cold  day,  each  register 
may  discharge  15  pounds  of  air  per  minute.     Suppose  there  are  8  such 
registers,  and  the  furnace  has  an  efficiency  of  60%.     If  all  this  air  is 
taken  in  from  out  of  doors  where  the  average  temperature  is  20°  F. 
and  heated  to  80°  F.,  how  much  coal  is  required  per  week? 

17.  Under  the  conditions  of  the  last  problem,  how  much  coal  is 
saved  per  week  if  four  fifths  of  the  air  that  circulates  through  the  fur- 
nace is  taken  from  the  house  at  an  average  temperature  of  70°,  and 
only  one  fifth  from  out  of  doors  ? 

PRACTICAL  EXERCISE 

Heat  value  of  coal.  If  a  Parr  bomb  calorimeter  is  available,  the 
heat  value  (B.t.u.  per  pound)  of  a  sample  of  coal  may  be  readily  de- 
termined. The  results  are  accurate  to  about  1  %.  Full  directions  for 
the  manipulation  and  calculation  are  furnished  with  the  instrument. 

196.  Melting  and  freezing.  If  a  pailful  of  snow  or  ice  is 
brought  in  from  out  of  doors  on  a  cold  winter  day  and  set 
on  a  stove,  one  finds  that  its  temperature  is  at  first  below  0°  C. 
and  slowly  rises  to  that  point.  It  then  remains  stationary, 
or  nearly  so,  until  all  the  snow  is  melted.  Then  the  tem- 
perature of  the  water  gradually  rises.  This  stationary  tem- 
perature, where  the  ice  (snow)  changes  to  water,  is  called  the 
melting  point  of  ice,  and  is  0°  C.,  or  32°  F. 

We  may  also  determine  the  freezing  point  of  water  by  making 
a  freezing  mixture  of  cracked  ice  and  salt  and  placing  it  in  a 
test  tube  containing  some  pure  water.  The  temperature  of 
the  water  will  be  observed  to  fall  slowly  until  the  water  begins 
to  freeze.  Then  the  temperature  remains  constant  until  all 
the  water  is  frozen.  This  stationary  temperature  at  which 
water  changes  into  ice  is  called  the  freezing  point  of  water,  and 
is  0°  C.,  or  32°  F. 

Substances  which  are  crystalline,  such  as  ice  and  many  metals, 
change  into  liquids  at  a  definite  temperature,  and  the  melting 


EXPANSION  IN  FREEZING  231 

point  of  such  a  substance  is  the  same  as  its  freezing  point. 
Non-crystalline  substances,  such  as  iron,  glass,  and  paraffin, 
pass  through  a  soft,  pasty  stage  as  the  melting  point  is  ap- 
proached. In  the  case  of  some  substances,  such  as  the  fats, 
the  melting  point  is  not  the  same  as  the  freezing  point.  Thus 
butter  will  melt  between  28°  and  33°  C.  and  yet  solidifies  be- 
tween 20°  and  23°  C. 

TABLE  OF  MELTING  OR  FREEZING  POINTS 


Platinum 

1755°  C 

Tin       .     .     . 

.     .     .     .     232°  C. 

Steel 

1300  to  1400°  C 

Sulfur 

115°  C 

Glass      .     .     . 
Cast  iron    .     . 
Copper 

1000  to  1400°  C. 
1100  to  1200°  C. 
1083°  C 

Naphthalene 
Paraffin     . 
Ice  . 

(moth  balls)     80P  C. 
.     .     about  54°  C. 
....        0°  C. 

Gold  .... 

.     .     .     1063°  C. 

Mercury   . 

„  .  .     .     .  -39°  C. 

Silver 

960°  C. 

Alcohol 

.    about  -112°  C. 

There  are  several  alloys  of  metals  which  melt  at  a  much  lower  tem- 
perature than  any  of  the  metals  of  which  they  are  made.  "  Wood's 
metal  "  (2  tin  -f-  4  lead  +  7  bismuth  +  1  cadmium  by  weight)  melts 
at  70°  C.,  although  the  lowest  melting  point  of  any  of  its  constituents, 
tin,  is  232°  C.  Wood's  metal  will  melt  even  in  hot  water.  Such 
alloys  are  used  to  seal  tin  cans  and  automatic  fire  sprinklers. 

197.  Expansion  in  freezing.  In  general,  when  a  liquid 
freezes,  it  contracts,  because  the  molecules  are  more  closely 
knit  together  in  the  solid  than  in  the  liquid  state.  But  when 
we  recall  that  ice  floats  and  pitchers  of  water  are  of  ten  cracked 
by  freezing,  we  see  that  water  expands  on  freezing.  In  fact, 
a  cubic  foot  of  water  becomes  1.09  cubic  feet  of  ice.  Cast  iron 
is  another  substance  that  expands  a  little  in  solidifying.  It  is 
therefore  adapted  to  making  castings,  for  in  this  way  every 
detail  of  the  mold  is  sharply  reproduced.  Of  course  allowance 
has  to  be  made  for  shrinkage  in  cooling.  In  making  good  type 
a  metal  is  needed  which  expands  a  little  on  solidifying ;  and  so 
an  alloy  of  lead,  antimony,  and  copper,  which  has  this  property, 
is  used. 


232 


WATER,   ICE,   AND  STEAM 


Fig.  227.  Expansive 
force  exerted  by 
freezing  water 
breaks  the  iron 
bomb. 


That  the  expansive  force  of  water  in  freez- 
ing is  enormous  can  be  seen  from  the  follow- 
ing experiment. 

Let  us  fill  a  cast-iron  bomb  with  water,  close 
the  hole  with  a  screw  plug  (Fig.  227),  and  put  the 
bomb  in  a  pail  of  ice  and  salt.  When  the  water 
in  the  bomb  freezes,  the  pressure  inside  increases 
more  and  more,  and  the  bomb  eventually  explodes. 

This  shows  why  water  pipes  and  automo- 
bile radiators  burst   on  nights   cold  enough 
to  freeze  the  water  in  them.     A  similar  pro- 
cess is  active  every  winter  in  breaking  the  rocks  of   moun- 
tains to  pieces.     Water  percolates  into  the  crevices,  freezes, 
and  expands. 

198.  Effect  of  pressure  on  melting  ice.  If  we  suspend  a  weight 
of  40  or  50  pounds  by  a  wire  loop  over  a  block  of  ice  (Fig.  228),  the  wire 
will  cut  slowly  through  the  ice.  The  pressure 
causes  the  ice  to  melt  under  the  wire ;  but  the 
water  flowing  around  the  wire  freezes  again 
above,  and  leaves  the  block  as  solid  as  before. 

This  experiment  shows  that  •  pressure 
causes  ice  to  melt  by  lowering  the  freez- 
ing point.  This  might  be  expected,  for 
pressure  on  any  body  tends  to  prevent  its 
expansion,  and  since  water  expands  on 
freezing,  pressure  tends  to  prevent  freez- 
ing ;  that  is,  it  lowers  the  freezing  point. 
It  requires,  however,  a  pressure  of  almost 
a  ton  (1850  pounds)  per  square  inch  to  lower  the  freezing 
point  1  degree  centigrade. 

In  skating,  the  high  pressure  under  the  edge  of  the  skate 
blade  melts  the  ice  and  forms  a  film  of  water  which  is  very  slip- 
pery. This  also  explains  how  snowballs  can  be  made  by  press- 
ing the  snow  between  the  hands.  The  pressure  at  the  points 
of  contact  between  the  flakes  of  snow  melts  them  and  then  the 


Fig.    228.     Wire   cutting 
through  a  block  of  ice. 


HEAT  OF  FUSION  233 

film  of  water  that  is  formed  freezes  again  when  the  pressure  is 
released.  The  flow  of  glaciers  of  solid  ice  around  corners  is 
explained  in  the  same  way. 

199.  Heat  required  to  melt  ice.     If  a  dish  of  ice  and  water 
at  0°  C.  is  kept  in  a  room  where  everything  else  is  at  0°,  the 
ice  will  not  melt  and  the  water  will  not  freeze.     But  if  the  dish 
is  surrounded  by  a  freezing  mixture,  such  as  salt  and  ice,  the 
water  will  freeze,  or  if  the  dish  is  brought  into  a  warm  room, 
the  ice  will  melt.     In  either  case,  however,  the  temperature  of  the 
mixture  will  remain  steadily  at  0°  until  either  all  the  ice  is 
melted  or  all  the  water  is  frozen. 

It  seems  evident,  then,  that  when  ice  melts,  heat  energy  is 
absorbed,  which  does  not  show  itself  in  a  rise  of  temperature. 
This  is  called  the  heat  of  fusion  of  ice,  or  the  latent  (or  hidden) 
heat  of  melting  ice. 

200.  How  much  heat  to  melt  1  gram  of  ice  ?    In  solving  this 
problem  we  may  apply  the  method  of  mixtures  which  was  used 
in  determining  the  specific  heat  of  a  metal. 

FOR  EXAMPLE,  if  we  put  200  grams  of  ice  at  0°  C.  into  300  grams  of 
water  at  70°  C.  and  stir  them  thoroughly,  the  temperature  of  the 
water,  after  the  ice  is  all  melted,  .will  be  10°  C. 

Let  x  =  no.  of  calories  required  to  melt  1  g.  of  ice. 

Then  200  x  =  no.  of  calories  required  to  melt  200  g.  of  ice. 

Also       200  X  10  =  no.  of  calories  required  to  raise  melted  ice  from  0° 

to  10° 
and  300(70  -  10)  =  no.  of  calories  given  out  by  the  water  in  cooling. 

Heat  units  taken  in  =   Heat  units  given  out. 
Then  200  x  +  200  X  10  =  300  (70  -  10) 

whence  x  =  80  calories. 

The  best  experiments  that  have  been  made  show,  that  the 
heat  of  fusion  of  ice  is  just  about  80  calories,  which  means  that 
80  calories  are  absorbed  in  changing  1  gram  of  ice  at  0°  C.  into 
water  at  0°  C. 

201.  Heat  given  out  when  water  freezes.     We  have  just 
seen  that  heat  energy  is  required  to  pull  apart  the  molecules 
of  the  solid  ice  and  change  it  into  the  liquid  state,  where  the 


234 


WATER,   ICE,   AND  STEAM 


molecules  are  held  together  less  intimately.  Now  we  wish  to 
show  that  in  the  reverse  process,  that  is,  in  freezing,  this  energy 
appears  again  as  heat.  We  may  show  that  freezing  is  a  heat- 
evolving  process  in  the  following  experiment. 

If  we  repeat  the  experiment  described  in  section  196,  except  that 
we  keep  the  water,  thermometer,  and  test  tube  (Fig.  229)  very  quiet, 
we  shall  be  surprised  to  find  that  the  water  will 
cool  several  degrees  below  0°  C.  before  the  freez- 
ing begins.  When  once  started  by  stirring  or 
dropping  in  an  ice  crystal,  freezing  goes  on 
rapidly ;  but  the  temperature  jumps  to  0°  C.  and 
remains  stationary  until  all  the  water  is  frozen. 
The  latent  heat  given  out  in  freezing  is  absorbed 
by  the  colder  freezing  mixture  in  the  jar  outside. 

People  sometimes  make  use  of  the  heat 
given  out  by  water  when  it  freezes,  by  put- 
ting pails  or  tubs  of  water  in  a  greenhouse 
or  a  cellar  to  prevent  the  freezing  of  the 
plants  or  vegetables.  As  the  water  begins 
to  freeze  first,  the  heat  evolved  in  the  pro- 
cess prevents  the  temperature  from  falling 
When  a  large  lake  freezes,  the  heat  evolved 


Fig.   229.       Freezing 
water  evolves  heat. 

much  below  0°  C. 


helps  to  keep  the  temperature  in  its  vicinity  from  falling  as  low 
as  it  does  farther  away. 

202.  How  melting  ice  is  used  in  a  refrigerator.  We  all  know  that 
a  refrigerator  is  merely  a  box  with  ice  in  the  top  (Fig.  230)  which  is 
used  to  keep  food  cool.  The  air  around  the  ice  is  cooled,  settles  down 
on  account  of  its  greater  density,  takes  up  heat  from  the  food  or  from 
the  walls,  and  rises  again,  as  indicated  by  the  arrows.  The  cooling 
of  the  air  is  due  almost  entirely  to  the  absorption  of  heat  by  the  ice  in 
melting.  Therefore,  a  refrigerator  in  which  ice  did  not  melt  at  all  (if 
there  were  such  a  one)  would  be  quite  useless.  Furthermore,  while 
a  fabric  cover  for  the  ice  may  be  a  good  means  of  saving  ice,  it  is  a 
poor  way  to  save  food.  On  the  other  hand,  it  is  not  economical  to  let 
ice  melt  in  a  refrigerator  merely  because  heat  leaks  in  through  the 
walls.  The  two  essentials  in  economical  refrigeration  are,  first,  that 
the  transfer  of  heat  from  the  food  to  the  ice  should  be  furthered  in 


QUESTIONS  AND  PROBLEMS 


235 


^Insulation 


every  way  possible;  and  second,  that  the  transfer  of  heat  from  the 
room  to  the  ice  should  be  hindered  in  every  way  possible.  The  first 
requires  free  and  unimpeded  con- 
vection currents  inside  ;  the  sec- 
ond requires  that  the  walls  should 
be  very  well  insulated,  and  that 
the  doors  should  be  tight  and 
should  never  be  left  open  longer 
than  is  absolutely  necessary. 

QUESTIONS  AND  PROBLEMS 

1.  How    many     calories    of 
heat    are   required   to   melt   20 
grams  of  ice  at  0°  C.  ? 

2.  How  much  heat  is  evolved 

in  cooling  and  freezing  12  grams  Circulation  of  air  in  refrigerator, 

of  water  originally  at  10°  C.? 

3.  How  much  water  at  100°  C.  will  be  needed  to  melt  300  grams  of 
snow  at  0°  C.,  and  raise  its  temperature  to  20°  C.? 

4.  How  many  grams  of  ice  must  be  put  into  300  grams  of  water 
at  35°  C.  to  lower  the  temperature  to  10°  C.  ? 

6.    If  a  500-gram  iron  weight  is  heated  to  250°  C.  and  placed  on  a 
block  of  ice,  how  many  grams  of  the  ice  will  be  melted  ? 

6.  How  many  times  as  much  heat  is  required  to  melt  any  quantity 
of  ice  as  to  warm  the  same  quantity  of  water  1°  C.  ?    To  warm  the  same 
quantity  of  water  1°  F.?     How  many  B.t.u.  are  required  to  melt  1 
pound  of  ice? 

7.  In  testing  two  refrigerators  the  following  results  were  obtained : 


Insulation 


ROOM  TEMPERATURE 

COLDEST  INSIDE 
TEMPERATURE 

WEIGHT  OF  ICE 
MELTED  PER  HOUR 

No.  1 
No.  2 

92.1°   F. 

91.8°  F. 

52.7° 
57.2° 

1.50  Ib. 

1.78  Ib. 

Which  would  you  consider  the  better  refrigerator  and  why?        « 

8.  If  the  price  of  ice  is  50  cents  per  hundred  pounds  and  the  price 
of  gas  is  $1.00  per  thousand  cubic  feet,  which  is  more  expensive,  to 
absorb  or  to  produce  heat? 


236 


WATER,   ICE,   AND  STEAM 


PRACTICAL  EXERCISE 

Testing  a  refrigerator.  In  Circular  No.  55  of  the  Bureau  of  Stand- 
ards, entitled  Measurements  for  the  Household,  on  page  53  are  given 
the  results  of  tests  of  nine  refrigerators.  Try  to  make  as  complete 
a  test  as  possible  of  the  refrigerator  in  your  own  home. 

203.  Process  Of  boiling  water.  Let  us  fill  a  round-bottomed 
flask  (Fig.  231)  half  full  of  water  and  put  through  the  stopper  a  thermom- 
eter, an  open  manometer,  and  an  outlet 
tube  for  the  steam.  At  first,  as  the 
water  is  heated,  the  air  which  is  dis- 
solved in  the  water  rises  to  the  surface 
in  little  bubbles.  Then  bubbles  of  steam 
form  at  the  bottom ;  but  these  collapse 
when  they  strike  the  upper,  cooler 
layers  of  water,  and  disappear,  causing 
the  rattling  noise  known  as  "  singing  " 
or  "  simmering."  When  the  bubbles 
of  steam  begin  to  reach  the  surface, 
the  water  is  said  to  "  boil."  It  will  be 
noticed  that  the  steam  in  the  flask  is 
as  clear  as  air,  but  as  it  leaves  the  out- 
let tube  it  condenses  and  forms  a  white 
cloud  or  mist. 

As  soon  as  boiling  begins,  the  ther- 
mometer, which  has  been  rising  rap- 
idly, reaches  100°  C.  and  remains  sta- 
Fig.  231.    Boiling  water  in  a  flask.'    tionary. 

If  we  partly  close  the  outlet  valve, 

the  manometer  shows  an  increase  of  pressure,  and  the  thermometer 
shows  a  corresponding  rise  in  the  temperature  of  the  boiling  water. 

Finally,  we  remove  the  burner,  let  the  water  cool  a  bit,  and  then 
connect  the  outlet  tube  with  an  aspirator,  which  reduces  the  pressure 
and  makes  the  water  boil  again. 

The  process  of  boiling  consists  in  the  formation  in  a  liquid 
of  bubbles  of  vapor,  which  rise  to  the  surface  and  escape.  The 
temperature  at  which  this  takes  place  is  the  boiling  point  of 
the  liquid. 

There  is  a  second  and  more  exact  definition  of  the  boiling 
point.  It  is  evident  that  a  bubble  of  water  vapor  can  exist 


VAPOR  PRESSURE 


237 


within  the  liquid  only  when  the  pressure  exerted  outward  by 
the  vapor  within  the  bubble  is  at  least  equal  to  the  atmos- 
pheric pressure  pushing  down  on  the  surface  of  the  liquid. 
For  if  the  pressure  within  the  bubble  were  less  than  the  out- 
side pressure,  the  bubble  would  immediately  collapse.  Now 
the  pressure  that  would  exist  inside  a  bubble,  if  it  could 
form  at  all,  would  be  different  at  different  temperatures.  It 
is  called  the  vapor  pressure,  or  vapor  tension,  of  the  liquid, 
and  we  shall  soon  see  how  to  determine  its  values  at  different 
temperatures.  The  boiling  point  of  a  liquid  may  therefore  be 
defined  as  the  temperature  at  which  its  vapor  pressure  is  one  at- 
mosphere. 

204.   Effect  of  changing  pressure.     The  following  interesting 
experiment  shows  water  boiling  under  reduced  pressure. 

Let    a  flask,   half-full   of   water   which   is   boiling   vigorously,   be 
removed  from  the  flame  and  instantly  corked  air-tight  with  a  rubber 
stopper.     We  may  then  invert  the  flask,  as 
shown  in  figure  232,  and  cool  the  top  by  pour- 
ing on  cold  water.     The  water  in  the  flask 
immediately  begins  to  boil  again.     This  is  be- 
cause the  steam  in  the  top  of  the  flask  is  con- 
densed and  so  the  pressure  on  the  surface  of 
the  liquid  is  much  reduced. 

The  last  two  experiments  have  shown 
that  if  the  pressure  on  the  surface  of  the 
liquid  is  increased,  the  temperature  has 
to  be  raised  before  the  liquid  will  boil, 
while  if  the  pressure  is  decreased,  the 
liquid  will  boil  at  a  lower  temperature. 
We  can  understand  this  if  we  recall  that 
ordinarily  the  atmosphere  is  exerting  a  lg'  un^er 
pressure  of  about  15  pounds  per  square 

inch  on  the  surface  of  the  liquid.  If  we  reduce  this  pressure,  it 
is  easier  for  the  bubbles  of  vapor  to  form ;  if  the  pressure  is 
increased,  it  is  more  difficult  for  the  bubbles  to  form.  In  any 


238 


WATER,   ICE,   AND  STEAM 


case,  they  will  form  only  when  the  temperature  is  high  enough 
so  that,  when  they  have  formed,  the  pressure  in  them  is  equal 
to  the  pressure  on  the  surface  of  the  liquid.  So,  by  observing 
the  temperatures  at  which  a  liquid  boils  under  different  pres- 
sures, we  can  determine  how  the  vapor  pressure  of  the  liquid 
changes  with  temperature.  Experiments  have  shown  that,  near 
100°  C.,  the  vapor  pressure  of  water  increases  by  about  27  milli- 
meters of  mercury  for  each  centigrade  degree  rise  of  temperature. 

The  following  table  shows  how  the  temperature  of  boiling  water 
changes  with  the  pressure  both  below  and  above  atmospheric  pres- 
sure. 

TEMPERATURE  OF  WATER  BOILING  AT  VARIOUS  PRESSURES 


Absolute 
pressure 
Lbs./sq.  in. 

Fahrenheit 
temperature 

Centigrade 
temperature 

Absolute 
pressure 
Lbs.  /  sq.  in. 

Fahrenheit 
temperature 

Centigrade 
temperature 

1 

102° 

39° 

20 

228° 

109° 

3 

142° 

61° 

25 

240° 

116° 

6 

170° 

77° 

30 

250° 

121° 

10 

193° 

90° 

40 

267° 

131° 

14.7 

212° 

100° 

50 

281° 

138° 

Since  we  have  defined  the  100°  point  on  the  centigrade  scale 
as  the  temperature  of  boiling  water,  and  since  the  temperature 
at  which  water  boils  is  so  much  affected  by  changes  in  pressure, 
it  is  necessary  to  fix  on  some  standard  pressure  at  which  ther- 
mometers are  to  be  "  calibrated,"  or  marked.  By  common 
agreement,  this  standard  pressure  is  the  pressure  exerted  by  a 
column  of  mercury  760  millimeters  high,  the  temperature  of 
the  mercury  being  0°  C.  The  temperature  at  which  water 
boils  under  this  pressure  is,  by  definition,  100°  C. 

205.  Applications.  Sometimes  it  is  very  desirable  to  boil  liquids  at 
as  low  a  temperature  as  possible.  For  example,  the  water  is  boiled 
away  from  sirup  and  from  milk  in  what  are  called  vacuum  pans,  which 
are  merely  closed  kettles  with  part  of  the  air  pumped  out.  The  water 
boils  away  at  about  70°  C.  and  leaves  the  granulated  sugar  or  milk 
condensed,  but  not  cooked. 

On  the  tops  of  high,  mountains  the  temperature  of  boiling  water  is 
so  low  that  eggs  cannot  be  cooked.  In  Cripple  Creek,  Col.,  about 


THE   PROCESS  OF  BOILING 


239 


10,000  feet  above  sea  level,  it  takes  about  twice  as  long  to  cook  potatoes 
as  in  Boston.  At  these  high  altitudes  closed  vessels  provided  with 
safety  valves,  called  "  digesters  "  or  "  pressure  cookers  "  (Fig.  233), 
have  to  be  used  in  cooking.  Such  kettles  are  also  needed  for  hastening 
the  cooking  of  certain  foods  and  for  the  rapid 
sterilization  of  products  that  are  to  be  canned. 
Digesters  are  commercially  used  for  extracting 
gelatin  from  bones.  The  effect  of  the  increased 
pressure  in  a  digester,  or  pressure  cooker,  is  the 
same  as  in  a  boiler.  The  water  in  a  boiler  whose 
gauge  reads  100  pounds  is  boiling,  not  at  100°  C., 
but  at  170°  C.,  or  338°  F. 


Fig.  233.  Pressure 
cooker  for  domestic 
use. 


206.  Summary.     What    has    been    said 
about  the  process  of  boiling  can   be   sum- 
marized as  follows : 

(1)  A  liquid  will  boil  only  when  its  tem- 
perature  is    such  that  its  vapor  pressure  is  equal  to  the  pres- 
sure on  its  surface. 

(2)  What  is  called  "  the  boiling  point  "  of  a  liquid  is  the  tem- 
perature at  which  it  will  boil  under  atmospheric  pressure;    that 
is,  the  temperature  at  which  its  vapor  pressure  is  one  atmosphere, 
or  760  millimeters  of  mercury. 

(3)  Every  liquid  has  its  own  boiling  point.     The  boiling  point 
of  water  is  by  definition  100°  C. 

(4)  The  rule  about  boiling  under  other  pressures  than  one 
atmosphere  is,  the  higher  the  pressure,  the  higher  the  temperature 
required  to  make  the  liquid  boil. 

TABLE  OF  BOILING  POINTS 

(At  a  pressure  of  760  millimeters) 

Zinc 918°  C. 

Sulfur 445°  C. 

Mercury 357°  C. 

Saturated  salt  solution   .  108°  C. 

Water 100°  C. 

207.  Distillation.     In  many  localities  the  only  way  to  be 
sure  of  getting  pure  water  is  by  what  is  called  distillation. 


Alcohol 

.     .     .       78°  C. 

Ether 

.     .     .       35°  C. 

Ammonia     .     . 
Oxygen   .     .     . 
Hydrogen    .     . 

.      -    34°  C. 
.      -  183°  C. 
.      -  253°  C. 

240 


WATER,  ICE,   AND  STEAM 


Faucet 

t=< — 
Water 


The  water  is  boiled  in  a  vessel  which 
is  so  arranged  that  the  steam  will 
pass  through  a  cold  tube  and  again 
return  to  the  liquid  condition  (Fig. 
234).  This  change  of  water  vapor  to 
liquid  water  is  called  condensation, 
and  the  apparatus  in  which  it  takes 
place  is  called  a  condenser.  The 
water  which  drops  from  the  end  of 
the  condenser  is  pure,  the  impurities 
being  left  behind  in  the  vessel  in  which 
the  water  was  boiled. 


Fig.  234.     Purification  of  water  by 
distillation. 


The  process  of  distillation  con- 
sists of  boiling  a  liquid  and  con- 
densing its  vapor.  In  commercial 
work  this  is  usually  done  in  a 
"  worm  condenser."  This  con- 
sists of  a  pipe  coiled  into  a  spiral 
and  surrounded  by  circulating 
cold  water  (Fig.  235).  In  this 
way  a  large  condensing  surface  is 
obtained  in  a  small  space. 

When  a  mixture  of  two  liquids  is 
distilled,  the  vapor  formed  contains 
much  more  of  the  substance  with 
the  lower  boiling  point  than  did 
the  original  mixture.  This  sub- 
stance can  thus  be  more  or  less 
completely  separated  from  the  one 
with  the  higher  boiling  point.  It 
is  by  this  process  of  fractional 
distillation  that  gasoline  and  kero- 
sene are  obtained  from  crude  pe- 
troleum. Gasoline  distills  over  be- 
tween 70°  and  120°  C.  and  kerosene  ,  ^  "*** Water 

.  Fig.  235.     Worm  condenser  offers 

between  150    and  300    C.  a  large  cooling  surface. 


HEAT  OF   VAPORIZATION  241 

QUESTIONS  AND  PROBLEMS 

1.  How  is  the  temperature  of  boiling  water  affected  by  taking  the 
water  to  the  bottom  of  a  deep  mine? 

2.  If  water  boils  at  99°  C.,  what  is  the  atmospheric  pressure? 

3.  If  water  boils  at  208°  F.,  what  does  the  barometer  read? 

4.  An  elevation  of  900  feet  makes  a  difference  of  about  1  inch  in  the 
barometer.     At  what  temperature  would  water  boil  1500  feet  above  the 
sea? 

6.  In  Altman,  Colorado,  which  is  one  of  the  highest  towns  in  the 
country,  the  temperature  of  boiling  water  is  about  88.5°  C.  What  is 
the  altitude  (approximately)  ? 

6.  Plot  a  vapor-pressure  curve  for  water,  laying  off  temperatures 
horizontally  and  pressures  vertically.     (Hint :    Use  5  small  divisions 
for  10°  F.,  or  10  small  divisions  for  10°  C.,  and  use  20  small  divisions 
for  10  pounds  per  square  inch.) 

7.  A  certain  pressure  cooker  is  designed  to  cook  at  20  pounds  of 
steam  pressure  above  atmospheric  pressure.     What  is  the  temperature 
inside  ? 

8.  What  effect  does  salt  or  sugar  have  on  the  boiling  point  of  water  ? 
Try  it. 

9.  What  effect  does  a  little  denatured  alcohol  have  on  the  boiling 
point  of  water?     Try  it.    What  bearing  does  this  have  on  the  use  of 
alcohol  in  automobile  radiators  in  winter  ? 

10.  In  distilling  petroleum,  some  of  the  products  are  petroleum 
ether,  gasoline,  naphtha,  and  kerosene.     Which  distills  over  first? 

11.  Mark  Twain  in  his  "  Tramp  Abroad  "  tells  of  stopping  on  his 
way  up  a  mountain  to  "  boil  his  thermometer."     What  did  he  do,  and 
why? 

208.  Heat  of  vaporization  of  water.  When  a  kettle  of  water 
is  put  on  a  stove,  it  gets  hotter  and  hotter  until  it  boils.  Then, 
no  matter  how  much  heat  we  apply  to  the  kettle,  if  there  is  a  free 
outlet  for  the  steam  to  escape,  the  temperature  remains  con- 
stant at  100°  C.,  or  212°  F.  The  heat  energy  which  seems  to 
disappear  in  boiling  the  water  is  called  the  heat  of  vaporization 
or  the  latent  heat  of  steam.  This  heat  of  vaporization  is 
the  energy  needed  to  pull  the  molecules  of  water  away  from 
each  other  and  set  them  free  as  steam. 


242 


WATER,   ICE,   AND  STEAM 


209.  How  much  heat  is  needed  to  make  a  gram  of  steam? 
When  we  want  to  determine  the  amount  of  heat  needed  to 
change  a  gram  of  water  at  100°  C.  into  steam  at  100°  C.,  we 
use  the  method  of  mixtures,  and  instead  of  measuring  the  heat 
absorbed  in  making  steam,  we  measure  the  heat  given  off  when 
steam  condenses. 

FOR  EXAMPLE,  suppose  we  take  400  grams  of  water  at  5°  C.  and 
run  in  enough  dry  steam  at  100°  C.  to  raise  the  temperature  of  the 
water  to  35°  C.  We  then  find  by  weighing  that  we  have  420  grams 
of  water,  showing  that  20  grams  of  steam  were  condensed.  How  many 
calories  of  heat  are  given  out  by  1  gram  of  steam  in  condensing  to 
water  at  100°  C.  ? 

Let  x  =  heat  of  vaporization. 

Then    400(35  -  5)  =  heat  absorbed  by  cold  water, 

20  x  =  heat  given  out  by  condensing  of  steam, 
and     20(100  —  35)  =  heat  given  out  by  resulting  water  in  cooling  from 

100°  to  35°  C. 

Heat  units  absorbed  =  Heat  units  given  out, 
then  400(35  —  5)  =  20  x  +  20(100  -  35) 

and  x  =  535  calories. 

Recent  experiments  have  shown  that  the  heat  of  vapori- 
zation of  water  is  about  540  calories.  In  other  words,  it  takes 

more  than  five  times  as  much  heat 
to  change  any  quantity  of  water  into 
steam  as  to  raise  the  same  quantity 
of  water  from  the  freezing  to  the 
boiling  point.  In  English  units  it 
requires  540  X  1.8,  or  972  B.t.u.  to 
change  a  pound  of  water  at  212°  F. 
into  steam  at  212°  F. 

210.  Steam  heating.  The  fact  that 
the  heat  of  vaporization  of  water  is 
so  much  larger  than  the  heat  it  gives 

out  while  cooling  through  any  prac- 
Fig.  236.     Steam-heated  soup       .  ,  , 

kettle  tical  temperature   range  shows  why 


STEAM   HEATING 


243 


steam  is  so  much  used  for  heating.  Steam  is  formed  in  a  boiler, 
each  pound  of  water  absorbing  something  like  1000  B.t.u.  as  it  is 
warmed  and  vaporized.  The  steam  is  piped  to  the  place  where 
heat  is  desired  and  is  then  condensed,  giving  out  the  1000  B.t.u. 
again.  The  hot  water  formed  by  the  condensation  then  runs 
back  into  the  boiler  by  gravity.  The  pressure  in  such  a  system 
is  commonly  only  a  few  pounds  above  atmospheric. 

In  the  kitchens  of  hotels  and  large  restaurants,  soups  and  chowders 
are  made  and  vegetables  are  boiled  in  great  dpuble-walled  copper 


Tempering        \  By  pass 
coils.  dampe 


Fig-  237-    Diagram  of  indirect  heating  system. 

kettles  (Fig.  236),  the  contents  of  which  are  heated  by  admitting  steam 
to  the  space  between  the  walls.  In  sugar  refineries  the  sirup  is  boiled 
down  by  condensing  steam  in  coils  immersed  in  vats  of  the  liquid.  In 
both  cases  the  temperature  at  which  the  process  is  carried  on  can  be 
controlled  and  held  constant,  as  closely  as  may  be  desired,  by  passing 
the  incoming  steam  through  a  reducing  valve  that  admits  fresh  steam 
just  fast  enough  to  keep  the  pressure  of  the  condensing  steam  constant. 
Factories,  office  buildings,  hotels,  schoolhouses,  and  other  large 
buildings  are  usually  heated  by  steam  which  is  formed  in  one  or  more 
boilers  in  the  basement.  Sometimes  the  steam  is  condensed  in  radia- 
tors in  the  various  rooms ;  more  often  it  is  condensed  in  coils  or  grids 


244 


WATER,  ICE,   AND  STEAM 


of  pipe  over  which  fresh  air  is  drawn,  thus  providing  for  ventilation 
as  well  as  heating.  Such  a  system  is  called  indirect  heating  (Fig.  237). 
When  radiators  are  used,  they  are  likely  to  become  air-bound;  air 
gets  into  the  system  when  it  is  not  in  use,  or  is  introduced  in  solution 
in  the  water  fed  to  the  boiler  and  tends  to  collect  in  the  radiators. 
Then  it  quickly  cools  off  and  prevents  steam  from 
entering.  This  difficulty  is  overcome  automatically  by 
a  small  air  vent  on  each  radiator.  In  one  type  of 
vent  (Fig.  238)  there  is  an  ebonite  rod  A  which,  when 
cool,  is  short  enough  to  leave  the  hole  at  the  top  open 
so  that  the  entrapped  air  can  escape.  When  hot  steam 
reaches  the  ebonite,  it  lengthens  and  closes  the  valve. 
If  water  reaches  the  vent,  the  bell  B,  which  always  con- 
tains some  air,  floats  and  closes  the  valve. 

As  a  means  of  heating  dwellings,  the  system  de- 
scribed above  is  inconvenient,  because   the  tempera- 


Fig.  238 

matic 


*.       ture  of  steam  condensing  at  atmospheric  pressure  is 


tor  vent.  212°  F.,  and  this  makes  the  radiators  much  too  hot 

in  mild  weather.  This  difficulty  is  overcome  in  the 
so-called  "vapor"  systems  by  purposely  letting  the  radiators  stay 
air-bound,  only  enough  air  .being  bled  off  to  keep  a  suitable  part  of 
each  radiator  active.  In  such  systems  the  radiators  have  no  air 
vents,  but  at  the  outlet  from  each  radiator  there  is  a  valve  which 
passes  either  air  or  condensed  water,  but  not 
steam.  A  valve  like  figure  238  would  do  this  if 
the  bell  were  left  out ;  another  type  is  shown  in 
figure  239.  This  type  contains  an  air-tight  cop- 
per box  with  corrugated  sides.  When  this  box  is 
made,  a  bit  of  blotting  paper  soaked  in  gasoline 
is  put  inside  and  the  box  is  then  sealed  up. 
When  the  box  is  surrounded  by  hot  steam,  the 
vapor  pressure  of  the  gasoline  inside  stretches 
the  box  and  this  closes  the  valve.  Either  water 
or  ah*  is  so  much  cooler  than  steam  that  the  box 
contracts  and  the  valve  opens. 

In  factories,  the  vacuum  system  of  steam  heat- 
ing is  often   used.    The  whole  system  is  made 

air-tight,  and  a  vacuum  pump  is  installed  which  pumps  both  air  and 
water  out  through  the  return  pipes  so  as  to  maintain  a  partial  vacuum 
in  the  radiators.  If  the  remaining  pressure  in  the  radiators  is  one 
third  of  an  atmosphere,  the  temperature  of  the  condensing  steam  is 
about  161°  F. ;  and  if  the  pressure  is  only  one  tenth  of  an  atmosphere 


To  return  pipe 

Fig.  239.    Water  and 
air  relief  trap. 


PROBLEMS  245 

the  temperature  is  only  about  115°  F.    In  this  way  the  heating  ac- 
tion of  the  radiators  can  be  regulated  to  suit  the  weather. 

One  advantage  of  steam  heating  in  factories  is  that  it  can  be  com- 
bined with  a  power  plant,  the  steam  being  generated  at  high  pressure 
and  used  in  a  steam  engine  which  discharges  it  at  the  pressure  desired 
in  the  heating  system.  This  plan  gives  both  heat  and  power  at  a  total 
cost  only  a  little  greater  than  that  of  either  by  itself. 

PROBLEMS 

1.  Find  the  number  of  calories  required  to  change  15  grams  of  water 
at  100°  C.  into  steam. 

2.  How  many  calories  are  required  to  heat  a  kilogram  of  water 
from  20°  C.  to  100°  C.  and  convert  it  into  steam? 

3.  How  many  B.t.u.  are  needed  to  change  20  pounds  of  water 
at  40°  F.  into  steam  at  212°  F.  ? 

4.  Compute  the  heat  evolved  by  condensing  10  grams  of  steam  at 
100°  C.  and  cooling  it  down  to  50°  C. 

5.  How  much  heat  will  be  required  to  convert  1  kilogram  of  ice  at 
0°  C.  into  steam  at  100°  C.? 

6.  How  much  steam  at  100°  C.  must  be  run  into  500  grams  of  water 
at  10°  to  raise  it  to  40°? 

7.  A  swimming  pool  is  60  feet  long  and  30  feet  wide,  and  the  aver- 
age depth  of  the  water  is  5  feet.     Steam  at  212°  F.  is  run  in  to  raise 
the  temperature  of  the  water  from  63°  F.  to  68°  F.     How  many  pounds 
of  steam  are  needed? 

8.  In  the  illustrative  example  in  section  209,  the  heat  of  vapori- 
zation came  out  535,  which  is  a  little  too  low.     This  shows  that  the 
steam  was  not  dry.     How  much  of  the  steam  had  already  condensed? 

9.  A  certain  alcohol  stove,  designed  for  polar  expeditions,  was 
found  to  change  4  kilograms  of  ice  at  —40°  C.  to  water  at  100°  C.  in 
10  minutes  by  burning  140  grams  of  alcohol.     If  the  heat  of  combus- 
tion of  denatured  alcohol  is  6000  calories  per  gram,  and  if  the  specific 
heat  of  ice  is  0.5,  what  was  the  thermal  efficiency  of  the  stove? 

10.  How  many  pounds  of  coal  will  be  needed  in  a  boiler  whose  effi- 
ciency is  65%  to  convert  100  pounds  of  water  at  50°  F.  into  steam  at 
212°  F.?  Assume  that  the  heat  value  of  the  coal  is  14,500  B.t.u.  per 
pound. 


246  WATER,  ICE,   AND  STEAM 

PRACTICAL  EXERCISES 

1.  Pressure  cooker.  Attach  a  thermometer  to  the  cover  of  a  pres- 
sure cooker.  Fill  the  kettle  about  one  third  full  of  water  and  heat  the 
water  till  the  thermometer  indicates  a  little  over  212°  F.  Then  stop 
heating,  open  the  safety  valve,  and  let  out  the  air.  Now  heat  again 
and  record  the  temperature  for  each  two  pounds  increase  of  pressure 
up  to  20  pounds  per  square  inch.  Heat  slowly.  Plot  your  results 
as  a  curve  and  compare  with  the  table  on  page  238. 

2.  Steam-heating  plant.  Study  the  boilers  in  the  heating  plant  of 
the  school  building,  an  apartment  house,  or  a  factory.  What  kind 
of  fuel  is  used?  Where  does  the  water  come  from?  How  is  the  water 
heated?  What  three  safety  devices  are  attached  to  the  boiler?  Is 
the  steam  distributed  through  a  one-pipe  or  a  two-pipe  system  ?  How 
are  the  rooms  ventilated? 

211.  Evaporation.     Everyone  is  familiar  with  the  fact  that 
water  left  in  an  open   dish   gradually  disappears,  or  evapo- 
rates.   Evaporation  is  different  from  boiling,  in  that  evaporation 
takes  place  at  any  temperature,  but  only  at  the  surface  of  a 
liquid ;    while  boiling  goes  on  inside  the  liquid,  but  only  at  a 
fixed  or  definite  temperature.     Evaporation  goes  on  more  rapidly 
the  warmer  and  drier  the  surrounding  air  is.    For  example,  wet 
clothes  dry  more  quickly  on  a  hot  day  than  on  a  cold,  foggy 
day. 

212.  Cooling  by  evaporation.     If  one  pours  a  few  drops  of 
alcohol  or  ether  on  one's  hand,  the  liquid  quickly  evaporates, 
causing  a  marked  sensation  of  cold.     Whenever  a  liquid  evapo- 
rates, it  must  get  heat  from  somewhere,  and  so  the  temperature 
of  the  liquid  itself  and  of  anything  near  it  drops.     That  is  to  say, 
heat  is  absorbed  in  the  process  of  evaporation.     It  is  always  more 
comfortable  on  a  hot  day  to  ride  in  a  car  than  to  sit  still,  because 
the  rapid  circulation  of  the  air  makes  the  moisture  of  the  skin 
evaporate  more  rapidly.     This  is  why  one  can  tell  the  direction 
of  the  wind  by  lifting  a  moistened  finger ;  the  wind  blows  from 
the  side  which  feels  cool. 

213.  Moisture  in  the  air.     In  the  summer  time  the  outside 
of  a  pitcher  of  ice  water  is  usually  covered  with  drops  of  water. 


RELATIVE  HUMIDITY  247 

It  might  at  first  be  thought  that  these  were  due  to  the  water 
oozing  through  pores  in  the  side  of  the  pitcher ;  but  the  micro- 
scope does  not  show  any  pores  in  glazed  porcelain  or  glass,  so  we 
must  conclude  that  the  drops  come  from  the  surrounding  air. 
The  air  is  cooled  by  coming  in  contact  with  the  cold  pitcher  and 
deposits  some  of  its  moisture.  If  we  put  a  little  water  in  a 
bottle  and  cork  it  tightly,  the  water  does  not  evaporate  because 
the  air  above  the  water  quickly  becomes  "  saturated  "  with 
moisture.  Thus  we  see  that  air  can  take  up  only  a  definite 
quantity  of  moisture,  depending  on  the  temperature. 

Let  us  place  a  little  water  in  a  thin-walled  flask  and  cork  it.  If  we 
place  the  flask  in  the  sun  or  in  an  oven  until  it  becomes  warm,  and  then 
cool  it,  its  walls  become  dim,  because  of  the  drops  of  water.  The  warm 
saturated  air  becomes  "'  supersaturated  "  on  cooling. 

Careful  experiments  show  that  a  cubic  meter  of  saturated 
air  contains  at  different  temperatures  the  following  amounts 
of  water  vapor : 

2'grams  at    - 10°  C.  17  grams  at    20°  C. 

5  grams  at         0°  C.  30  grams  at    30°  C. 

9  grams  at       10°  C.  597  grams  at  100°  C. 

From  this  table  it  will  be  seen  that  air,  which  is  saturated 
at  one  temperature,  can,  at  a  higher  temperature,  take  up  still 
more  water  vapor  before  becoming  saturated ;  but  if  cooled,  it 
must  deposit  some  of  the  water  vapor  which  it  already  has. 

After  a  shampoo  or  a  swim,  a  lady  finds  that  her  hair  dries  slowly 
because  the  air  near  all  the  wet  surfaces  quickly  becomes  almost 
saturated  with  moisture.  If  this  layer  of  saturated  air  is  continually 
replaced  by  dry  air,  as  in  a  breeze  or  when  a  fan  or  electric  blower  is 
used,  evaporation  and  drying  proceed  much  more  rapidly.  "  Electric 
towels  "  work  similarly  by  blowing  warm  air  on  one's  hands. 

214.  Relative  humidity.  Usually  the  air  does  not  contain 
all  the  moisture  which  it  can  hold ;  that  is,  it  is  not  saturated. 
If,  however,  the  temperature  suddenly  drops,  the  same  actual 
amount  of  moisture  will  saturate  the  air. 


248 


WATER,   ICE,   AND  STEAM 


If  the  water  in  a  polished  nickel-plated  cup  is  cooled  with  ice  below 
the  temperature  of  the  room,  a  mist  appears  on  the  outside  of  the  cup. 
The  temperature  of  the  water  when  this  occurs  is  the  "  dew  point." 

The  dew  point  is  the  temperature  at  which  the  water  vapor  in 
the  air  begins  to  condense.  If  the  air  is  cooled  below  the  dew 
point,  some  of  its  vapor  condenses,  and  dew  collects  on  objects. 
Thus  we  see  that  the  words  "  dry  "  or  "  moist,"  as  applied  to 
the  atmosphere,  have  a  purely  relative  significance.  They 
involve  a  comparison  between  the  amount  of  water  vapor 
actually  present,  and  that  which  the  air  could  hold  if  saturated 
at  the  same  temperature.  The  ratio  of 
these  two  quantities  is  called  the  rela- 
tive humidity.  For  example,  we  may 
read  in  the  newspaper  that  the  rela- 
tive humidity  is  85%.  This  means 
that  the  amount  of  water  vapor  actu- 
ally present  in  the  air  is  85%  of 
what  the  air  might  have  contained  at 
the  given  temperature  if  it  had  been 
saturated. 

215.  Wet-  and  dry-bulb  thermometers. 
Let  two  thermometers  be  arranged  as 
shown  in  figure  240.  The  bulb  of  the 
thermometer  at  the  left  is  dry,  while  the 
other  thermometer  has  its  bulb  covered 
with  a  cotton  wick  which  is  kept  moist  by  a 
cup  of  water.  If  we  keep  the  air  around 
the  thermometers  circulating  .by  an  electric 
fan,  after  a  little  while  the  wet-bulb  ther- 
mometer will  indicate  a  lower  temperature 
than  the  dry-bulb  thermometer.  This  cool- 
ing is  caused  by  the  evaporation  of  water  from  the  cotton  wick. 
The  drier  the  surrounding  air,  the  more  rapid  will  be  the  evaporation, 
and  so  the  greater  will  be  the  difference  between  the  wet-  and  dry- 
bulb  thermometers.  By  means  of  tables  furnished  with  the  instru- 
ment, we  may  determine  from  these  thermometer  readings  the  relative 
humidity  of  the  air. 


Fig.  240.  Wet-  and  dry-bulb 
thermometers  used  to  find 
humidity  of  air. 


DEW,   FOG,   RAIN,   AND  SNOW  249 

216.  Practical  importance  of  determining  humidity.     It  is 

well  known  that  a  hot  day  in  Boston  is  much  more  un- 
comfortable than  an  equally  hot  day  in  Denver.  This  is 
because  a  city  near  the  ocean,  like  Boston,  has  a  higher  relative 
humidity  than  a  city  which  is  inland  and  a  mile  above  sea  level, 
like  Denver.  When  the  relative  humidity  is  high,  we  feel 
"  sticky ,"  because  the  perspiration  of  the  skin  does  not  evap- 
orate readily.  On  the  other  hand,  too  little  humidity  is  in- 
jurious. Special  precautions  are  taken  to  keep  the  air  in 
schools,  hospitals,  private  houses,  and  especially  greenhouses 
from  getting  too  dry  in  winter.  In  cotton  mills  it  has  been 
found  that  the  air  must  be  rather  moist  to  make  the  spinning 
of  yarn  successful, 

Since  the  occurrence  of  frost  in  the  late  spring  or  early  fall 
is  injurious  to  many  crops,  it  is  often  highly  important  that 
farmers  should  know  in  the  afternoon  whether  freezing  weather 
during  the  night  is  to  be  expected.  The  temperature  of 
the  dew  point  gives  a  ready  means  of  predicting  how  low 
the  temperature  at  night  will  drop ;  for  when  the  dew  point 
is  reached,  further  cooling  is  retarded  by  the  heat  of  vaporiza- 
tion set  free  when  dew  forms.  If  the  dew  point  is  above  40°  F., 
the  temperature  will  but  seldom  fall  to  freezing  during  the 
night. 

217.  Dew,  fog,  rain,  and  snow.     On  clear,  still  nights  the 
ground  radiates  the  heat  that  it  has  received  during  the  daytime. 
The  grass  and  leaves,  which  can  radiate  heat  freely,  cool  rapidly 
and  soon  bring  the  air  near  them  below  its  dew  point.     Then 
moisture  condenses  as  dew  or  at  lower  temperatures  as  frost. 
This  phenomenon  is  exactly  like  the  formation  of  drops  of  water 
on  a  pitcher  of  ice  water,  or  on  one's  spectacles  when  one  comes 
from  the  cold  outdoors  into  a  warm  room.     Clouds  covering 
the  sky  hinder  the  formation  of  dew  because  they  lessen  radi- 
ation.    If  the  condensation  of  the  moisture  of  the  air  is  not 
brought  about  by  contact  with  cold  solid  objects  at  the  surface 
of  the  earth,  but  by  great  masses  of  cold  air  high  above  the 


250  WATER,   ICE,   AND  STEAM 

earth,  clouds  are  formed  and  rain  may  result.     Fog  is  merely 
a  cloud  touching  the  earth. 

Clouds  at  very  high  altitudes  may  be  composed  of  bits  of 
ice,  but,  in  general,  clouds  are  made  up  of  minute  drops  of 
water.  Like  particles  of  fine  dust,  very  small  drops  of  water 
tend  to  fall,  but  can  do  so  only  very  slowly.  Sometimes  they 
fall  into  warm  and  not  yet  saturated  layers  of  air,  and  then 
they  change  back  again  into  vapor.  Sometimes  they  are 
carried  up  by  ascending  currents  of  air  faster  than  they  can  fall 
through  them,  and  so  seem  to  float.  For  example,  the  cloud  of 


Fig.  241.     Snow  crystals. 

steam  above  a  locomotive  stack  is  composed  of  minute  drops 
of  water  and  yet  rises  with  the  warm  air.  Clouds  are  not 
durable.  They  simply  mark  a  place  in  the  atmosphere  where 
condensation  of  water  vapor  is  going  on.  In  rain  clouds  the 
little  particles  of  water  come  together  and  form  drops,  which 
easily  overcome  the  resistance  of  the  air  and  fall  to  the  ground. 
If  the  temperature  of  the  cloud  is  below  32°  F.,  the  particles  of 
water  unite  to  form  little  delicately  fashioned  hexagonal  snow 
crystals  (Fig.  241). 

Snow  and  rain  together  make  what  the  "  weather  man  " 
calls  "  precipitation."  Thus  in  New  York  there  are  about 
150  days  of  rain  or  snow  each  year,  and  the  total  precipitation 
in  a  year,  if  it  did  not  dry  up,  would  cover  the  earth  to  a  depth 
of  about  3  feet.  For  agriculture  it  is  necessary  to  have  an 
annual  total  of  eighteen  or  more  inches,  and  this  must  be  prop- 
erly distributed  throughout  the  year. 


PRACTICAL  EXERCISE  251 

QUESTIONS  AND  PROBLEMS 

1.  A  room  is  3  meters  high,  10  meters  long,  and  6  meters  wide. 
How  many  grams  of  water  will  be  required  to  saturate  the  air  at  20°  C.  ? 

2.  An  experiment  showed  that  on  a  certain  day,  when  the  tempera- 
ture was  30°  C.,  the  air  contained  12  grams  of  water  per  cubic  meter. 
What  was  the  relative  humidity  ? 

3.  How  do  undue  dryness  and  undue  dampness  affect  wooden 
furniture? 

4.  What  change  in  the  thermometer  usually  goes  with  a  rising 
barometer  ? 

6.   What  happens  when  a  moist  wind  from  the  ocean  strikes  a 
mountain  range? 

6.  In  some  hot  countries  the  people  cool  their  drinking  water  by 
setting  it  in  jars  of  porous  earthenware,  in  a  shady  place,  where  there  is 
a  current  of  air.     Explain. 

7.  Why  do  clothes  dry  best  on  a  windy  day? 

8.  Why  does  sprinkling  the  street  on  a  hot  day  cool  the  air? 

9.  Why  is  frost  more  likely  to  form  on  a  still  night  than  on  a  windy 
night? 

10.  Why  does  building  smudge  fires  in  an  orchard  tend  to  prevent 
frost? 

11.  Why  does  covering  plants  with  papers  tend  to  prevent  frost? 

PRACTICAL  EXERCISE 

Making  a  psychrometer.  Fasten  two  thermometers  to  a  narrow 
board  and  attach  a  strong  cord  to  the  upper  end  for  whirling  the  psy- 
chrometer about  your  head.  Fasten  a  single  wrapping  of  muslin  about 
one  bulb  and  moisten  with  water.  Whirl  the  thermometers  until  the 
wet  thermometer  ceases  to  fall.  Determine  the  relative  humidity 
from  these  readings  of  the  wet-  and  dry-bulb  thermometers  and  from 
the  table  which  is  furnished  with  the  thermometers  shown  in  figure 
240.  Find  the  humidity  (1)  on  a  clear  day;  (2)  on  a  damp,  cloudy 
day;  (3)  in  the  morning;  and  (4)  in  the  afternoon  of  a  clear  day. 
Make  a  record  of  all  your  data  and  results. 

218.  Freezing  by  boiling.  The  fact  that  a  large  quantity 
of  heat  is  needed  to  vaporize  a  substance  is  often  made  use 
of  in  getting  low  temperatures. 


252 


WATER,   ICE,   AND  STEAM 


If  a  cylinder  of  liquefied  carbon  dioxide  is  tilted,  as  shown  in  figure 
242,  and  the  valve  is  opened,  the  liquid  released  from  pressure  boils 
very  rapidly,  cooling  everything,  including  the  rest  of  the  liquid,  so 
much  that  some  of  it  is  frozen.  After  the  valve  has  been  open  a  short 

time,  the  bag  is  filled  with  a  white  solid, 
frozen  carbon  dioxide.  This  solid  evap- 
orates very  readily,  and  gives  a  tem- 
perature as  low  as  —  80°  C.  If  the 
solid  is  put  in  a  beaker  and  mixed  with 
ether,  the  mixture  will  freeze  a  test  tube 
of  mercury.  The  ether  serves  to  carry 
the  heat  quickly  from  the  test  tube  to 
the  solid. 


219.  Ice-making.  In  the  manu- 
facture of  ice  and  in  refrigerating 
plants  (Fig.  243),  gaseous  ammonia 
is  compressed  by  a  pump  and  then 
cooled  until  it  liquefies.  During 
this  process  of  compression  and  of 
condensation,  heat  is  evolved,  which 
is  removed  by  passing  the  ammonia  through  a  pipe  cov- 
ered with  running  water.  The  liquefied  ammonia  is  then 
piped  to  the  ice  tank  or  cold-storage  room,  and  allowed  to  ex- 


Expansion  valve -*\^~t       from 

Cold  storage 


Compressor  Brine  Tank  Brine  pump 


Fig.  243.     Diagram  of  an  ice-making  plant. 

pand  through  a  valve  with  a  small  opening.  This  checks  the 
flow,  and  so  enables  the  pump  to  maintain  enough  pressure  to 
keep  the  ammonia  in  liquid  form  on  its  way  to  the  valve  ;  while 


SUMMARY  253 

beyond  the  valve  the  pressure  is  very  small,  so  that  the  ammonia 
evaporates  rapidly.  While  doing  so,  it  absorbs  heat  from  the 
refrigerating  room.  It  is  then  ready  to  be  compressed  again. 

In  the  manufacture  of  ice,  the  expansion  pipes  pass  through 
a  brine  tank  in  which  are  smaller  tanks  of  pure  water.  When 
the  water  in  these  tanks  is  frozen,  the  tanks  are  pulled  up  and 
the  ice  removed.  The  ammonia  is  used  over  and  over  again, 
but  power  must  be  constantly  supplied  to  the  compressor. 

Iceless  refrigerators  for  home  use  also  have  a  small  com- 
pressor run  by  an  electric  motor,  cooling  coils,  an  expansion 
valve,  and  refrigerating  coils,  which  take  the  place  of  the  ice. 
Some  of  them  use  ammonia ;  others  use  methyl  chloride  or 
sulfur  dioxide  in  a  similar  way. 

SUMMARY    OF    PRINCIPLES    IN    CHAPTER   XI 

Heat  units : 

1  calorie     =  heat  to  raise  1  gram  of  water  1°  C. 
1  B.t.u.       =  heat  to  raise  1  pound  of  water  1°  F. 
Specific  heat  =  calories  to  raise  1  gram  of  substance  1°  C. 

=  B.t.u.  to  raise  1  pound  of  substance  1°  F. 
Specific  heat  of  water  =  1  in  either  system  of  units. 
Method  of  mixtures : 

Heat  given  up  by  hot  bodies  =  heat  absorbed  by  cold  bodies. 
Pressure : 

Lowers  freezing  point  of  water  0.0072°  C.  per  atmosphere. 
Raises  boiling  point  of  water  0.037°  C.  per  mm.  of  mercury. 
Heat  of  fusion  =  heat  absorbed  during  melting, 

=  heat  yielded  during  freezing. 
Value  for  water,  80  calories. 

Heat  of  vaporization  =  heat  absorbed  during  evaporation, 
=  heat  yielded  during  condensation. 
Value  for  water,  540  calories. 

actual  moisture  in  air 


Relative  humidity  = 


moisture  in  saturated  air  at  same  temp. 


254  WATER,  ICE,   AND  STEAM 

QUESTIONS 

1.  If  you  know  the  dew  point  to  be  10°  C.,  how  can  you  find  the 
relative  humidity  at  20°  C.  ? 

2.  Human  hair  when  treated  with  ether  is  very  sensitive  to  mois- 
ture.    When  it  is  moist  it  contracts,  and  when  it  dries  it  elongates. 
Explain  how  a  moisture  gauge,  or  "  hygroscope,"  could  be  made  with 
a  hair. 

3.  Could  gold  money  be  cast  instead  of  stamped  with  a  die? 

4.  Why  is  a  burn  from  live  steam  so  much  more  severe  than  one 
from  boiling  water  ? 

6.   Why  does  one  sometimes  "  catch  cold  "  by  sitting  in  a  draft 
of  cool  air  after  taking  violent  exercise? 

6.  How  low  can  the  temperature  fall  during  a  rain? 

7.  Why  can  mercury  mixed  with  zinc  be  purified  by  distillation  ? 

8.  Why  is  it  difficult  to  make  snowballs  out  of  "dry  snow"? 
What  is  "  dry  snow"? 

9.  What  is  the  scientific  fact  back  of  the  old  saying  that  "  a  watched 
pot  never  boils  "? 

10.  How  would  you  determine  the  coldest  spot  in  a  refrigerator? 
Which  foods  should  be  put  there? 

11.  Plot  a  curve  to  show  the  relation  of  calories  to  temperature  in 
changing  ice  at  -20°  C.  to  steam  at  120°  C.     (Make  the  scale  5  cal.  = 
1  mm.  horizontal  and  2°  =  1  mm.  vertical.) 

12.  Is  a  steam  vent  in  a  fireless  cooker  desirable?      Why? 

13.  Illustrate  from  home  experience  four  factors  affecting  rate  of 
evaporation. 

14.  Why  is  ebonite  chosen  for  the  rod  in  an  automatic  air  vent? 


PRACTICAL  EXERCISE 

Moisture  in  the  air  of  a  room.  Measure  the  dimensions,  tempera- 
ture, and  relative  humidity  of  your  schoolroom,  or  of  a  room  at  home, 
and  compute  the  total  weight  of  water  in  the  air  of  the  room. 

Pans  of  water  are  often  placed  over  hot-air  registers  or  hung  close 
to  radiators  to  humidify  the  air  in  the  room.  Try  to  find  out  how 
much  water  can  be  evaporated  per  hour  in  this  way,  and  how  much 
difference  it  makes  in  the  relative  humidity  of  the  room.  See  Packard, 
Humidity  Indoors  (School  Science,  March,  1922) 


CHAPTER  XII 


HEAT   ENGINES 

Importance  of  the  steam  engine  —  boilers  —  slide-valve  and 
Corliss  engines  —  condensers  —  efficiency  —  expansion  — 
cylinder  condensation  —  compounding  —  uniflow  engine  — 
steam  turbines  —  gas  engines  —  4-stroke  and  2-stroke  engines 
—  oil  engines  —  mechanical  equivalent  of  heat. 

220.  The  importance  of  the  steam  engine.  Until  about 
two  hundred  years  ago,  the  work  of  the  world  was  done  chiefly 
by  the  muscular  energy  of  men  and  of  animals,  and  occasionally 
by  windmills  and  water  wheels.  This  meant  that  no  very  large 
amount  of  power  was  available 
in  any  one  place,  and  useful 
things  were  made  in  small  quan- 
tities here  and  there  by  a  great 
many  independent  artisans,  each 
working  for  himself  or  with  a 
small  group  of  his  friends. 

The  first  successful  steam  en- 
gine was  made  in  1705  by  Thomas 
Newcomen,  an  English  black- 
smith ;  it  was  used  for  pumping 
water  out  of  a  coal  mine.  New- 
comen's  engine  (Fig.  244)  was 
very  crude  and  consumed  a  great 
deal  of  fuel  for  the  work  it  did, 
but  it  was  a  great  help  to  miners. 
Some  seventy  years  elapsed  with- 
out much  change  in  steam  engines.  But  then  a  Scotch  instru- 
ment maker  began  an  epoch-making  career  of  invention  and 

255 


Fig.  244. 


Newcomen' s  atmospheric 
steam  engine. 


256 


HEAT  ENGINES 


improvement,  that,  in  a  single  lifetime,  gave  to  the  world  almost 

every  essential  feature  of  the  steam  engine  of  to-day.     That 

man  was  James  Watt  (Fig.  245). 

There  resulted  a  tremendous  change  in  the  manner  of  life  of 

the   whole   civilized  world.     Large   amounts   of   power  could 

be  concentrated  in  a  single 
plant,  and  this  led  inevitably 
to  the  factory  system  and 
ultimately  to  quantity  pro- 
duction, like  that  of  the 
Ford  plant,  which  turns  out 
over  4000  automobiles  a  day. 
Railroads  and  steamboats 
were  developed  to  bring  all 
parts  of  the  world  far  closer 
together  than  ever  before. 
And  on  the  other  hand,  the 
factory  system  has  crowded 
out  the  independent  artisan 
and  given  us  the  labor  prob- 
lems of  to-day.  In  all  these 

Fig.  245.     James  Watt  (1736-1819).    In-  f^      ofPom   engine   has 

strument  maker  at  Glasgow  University,     Wa^S 

famous  for  his  improvements  on  the     affected     human     life     much 
steam  engine.  more     than     any    Qther    Qne 

machine  or  device  ever  invented. 

221.  A  modern  steam  plant.     In  a  modern  steam  plant  the 
steam  is  made  in  a  boiler,  is  used  in  a  steam  engine,  and  is 
usually  discharged  into  the  air  or  into  a  condenser.     We  shall 
discuss  these  in  turn. 

222.  Types  of  steam  boilers.     A  good  boiler  should  have 
great  capacity  for  its  bulk,  and  high  efficiency.     The  capacity 
of  a  boiler  means  the  amount  of  steam  it  can  make  per  hour. 
For  example,  a  modern  freight  locomotive  makes  over  50,000 
pounds  of  steam  an  hour.     Now  the  capacity  of  a  boiler  depends 
largely  on  the  amount  of  heating  surface  it  has,  because  only 


TYPES  OF  STEAM   BOILERS 


257 


about  so  much  heat  can  flow  per  hour  through  each  square 
inch  of  the  wall  between  the  fire  and  the  water.     For  this  reason 


S/eam 


Fig.  246.  Cross  section  of  a  modern  locomotive.  G,  grate  ;  B,  firebox ;  A,  brick 
arch  to  protect  tubes  from  direct  heat ;  ^P,  fire  tubes ;  L,  throttle  lever ; 
R,  throttle  rod;  T,  throttle  valve  ;  E,  exhaust  pipe  ;  V,  piston  valve  ;  C,  cylinder. 

boilers  are  often  made  in  very  complicated  shapes,  so  as  to 
have  as  much  heating  surface  as  possible. 

A  locomotive  boiler  (Fig.  246)  is  a  fire-tube  boiler.  This  is  a  cylin- 
drical shell  filled  with  tubes,  3  or  4  inches  in  diameter,  through  which 
the  fire  and  smoke  pass.  The  water  and  steam  fill  the  rest  of  the 
shell  outside  the 
tubes.  Modern 
power  plants  use 
water-tube  boil- 
ers (Fig.  247), 
which  have  the 
water  inside  the 
tubes  and  the  fire 
and  smoke  out- 
side. The  tubes  of 
such  boilers  are 
more  or  less  in- 
clined, and  are 
fastened  at  each 
end  into  pas- 
sages ("head- 
ers") which  lead 
to  a  drum  above ; 


Fig.  247.     Water-tube  boiler  with  superheater. 


the  tubes,  headers,  and  the  lower  part  of  the  drum  are  full  of  water ; 
the  remainder  of  the  drum  forms  a  space  for  steam.    The  fire  is  placed 


258 


HEAT  ENGINES 


under  the  front  end  of  the  tubes;  the  products  of  combustion  are 
deflected  by  brick  walls  so  that  they  have  to  pass  over  the  tubes  two 
or  three  times  before  escaping  up  the  chimney. 

One  improvement  in  modern  boilers  is  the  automatic  stoker, 
which  feeds  coal  into  the  grate  a  little  at  a  time  as  it  is  needed. 
When  the  coal  is  pushed  in  from  below,  as  shown  in  figure  248, 
the  device  is  called  an  underfeed  stoker.  In  some  plants,  coal 
,  is  crushed  to  a  dust  and  then  blown  in  and  burned  at  once. 
Sometimes  fuel  oil  is  sprayed  in  and  burned  under  the  boiler ; 
this  saves  the  expense  of  stokers  and  eliminates  the  ashes. 


Fig.  248.    Underfeed  automatic  stoker,  which  gives  smokeless  combustion. 

223.  Boiler  draft.  The  capacity  of  a  boiler  also  depends 
on  the  draft  which  is  available  to  make  the  fire  burn  fiercely. 
It  takes  about  20  pounds  of  air  to  burn  1  pound  of  coal.  To 
get  a  good  draft,  tall  chimneys  are  sometimes  used,  and  at 
other  times  a  forced  draft  is  made  by  a  big  fan.  On  battle- 
ships a  forced  draft  is  often  obtained  by  making  the  whole 
fireroom,  within  which  the  stokers  work,  air-tight,  and  keeping 
it  full  of  air  under  pressure,  supplied  by  blowers  or  pumps  as 
fast  as  it  can  escape  through  the  fires. 


BOILER  ACCESSORIES  259 

224.  Efficiency  of  boilers.     Just  as  with  any  machine,  the 
efficiency  of  a  boiler  is  the  output  divided  by  the  input.     In 
this  case  the  output  is  the  heat  in  the  steam  delivered,  and  the 
input  is  the  heat  in  the  coal  used.     The  efficiency  of  modern 
boilers    ranges    from    60    to    75  %.     The    hot    gases    in    the 
chimney  carry  off  a  great  deal  of  heat.     A  smaller  amount  of 
heat  is  lost  by  radiation  from  the  fire  box  and  boiler  setting. 
Smoke  pouring  from  the  chimney  means  that  just  so  much  un- 
consumed  fuel  is  going  to  waste,  and,  what  is  worse,  is  adding 
to  the  dirt  in  the  atmosphere  of  the  neighborhood. 

225.  Boiler  accessories.     Every  boiler  is   equipped   with   a   steam 
gauge,  which  is  merely  a  Bourdon  pressure  gauge  (section  76),  and  also 
a  water  gauge  (section  61),  which  enables  the  engineer  in  charge  to 
watch  the  water  level  in  the  boiler.     If  the  water  level  is  too  low, 
there  is  danger  of  burning  the  tubes 

and  plates  and  perhaps  of  wrecking 
the  boiler ;  if  it  is  too  high,  water  is 
liable  to  be  carried  along  with  the 
steam   and   so  damage  the    engine. 
Besides  these  devices,    every  boiler 
has  a  safety  valve,  which  automati-    pjg   249     Safety  valve  for  a  boiler, 
cally  blows  off  steam  when  the  pres- 
sure exceeds  a  certain  limit.     A  simple  form  of  safety  valve  is  shown  in 
figure  249.     In  some  forms  a  spring  is  set  so  as  to  release  some  steam 
if  the  pressure  becomes  too  great  inside  the  boiler. 

QUESTIONS 

1.  Which  type  of  boiler  is  ordinarily  used  with  the  small  "  donkey  " 
engines  that  operate  derricks? 

2.  Which  type  of  boiler  is  used  on  a  steam-driven  automobile? 

3.  How  does  the  principle  explained  in  section  181  apply  to  the 
water-tube  boiler  in  figure  247  ? 

4.  In   some  marine  boilers,  called   Scotch  boilers,  the  fire  box  is 
inside  the  shell  and  completely  surrounded  by  water  except  where  the 
coal  and  ash  doors  are.     What  is  the  advantage  of  this  type  of  con- 
struction? 

5.  How  much  of  the  fire  box  of  a  locomotive  is  surrounded  by 
water  ? 


260 


HEAT  ENGINES 


226.   Two  types  of  steam  engine.     The  engine  most  commonly 
used  in  small  plants  is  the  slide-valve  engine  (Fig.  250).     Steam 

comes  from  the  boiler 
into  the  steam  chest  C, 
and  then  into  the  work- 
ing end  A  of  the  cylinder 
through  a  passage  shown 
by  the  arrows  at  the 
right  of  the  picture.  At 
the  same  time  the  spent 
steam  in  the  other  end  B 
of  the  cylinder  is  pass- 
ing through  the  hollow 
interior  of  the  valve,  to 


Fig.  250.     Slide-valve  steam  engine. 


the  exhaust  passage  E. 

It  then  escapes  to  the 
air,  or  to  the  condenser,  through  a  pipe  at  the  back,  not  shown 
in  the  figure.  At  the  end  of  the  stroke  the  valve  is  pulled  far 
enough  to  the  right  to  admit  li ve  steam  to  the  left-hand  end  of 
the  cylinder,  while 
the  spent  steam  in 
the  right-hand  end 
escapes  into  the  ex- 
haust. The  slide 
valve  is  pushed 
back  and  forth  by  a 
so-called  eccentric. 
This  is  a  circular 
disk  which  is  set 
on  the  main  shaft 
a  little  off  center. 


Fig.  251.     Corliss  steam  engine. 


The  wobbling  motion  of  the  eccentric  is  communicated  to  the 
slide-valve  rod  by  means  of  a  collar. 

In  large  steam  engines  Corliss  valves  are  more  often  used. 
A  Corliss  valve  (Fig.  251)  opens  and  closes  by  turning  a  little 


EFFICIENCY  OF  A   STEAM  PLANT  261 

in  its  seat.     In  a  Corliss  engine  there  are  four  such  valves 

two  at  each  end  of  the  cylinder.  Two  of  them,  N  and  0, 
are  for  admitting  the  steam,  and  two,  P  and  Q,  for  letting  the 
steam  out.  When  valve  N  is  open  to  admit  steam,  valve  Q  is 
also  open  to  let  steam  out  of  the  other  end  of  the  cylinder, 
while  0  and  P  are  closed ;  on  the  reverse  stroke,  0  and  P  are 
open,  while  N  and  Q  are  closed.  These  valves  are  auto- 
matically opened  and  closed  at  the  proper  time  by  the  engine 
itself.  The  fact  that  the  time  at  which  each  valve  opens  can 
be  accurately  adjusted  independently  of  the  other  valves  makes 
Corliss  engines  more  efficient  than  slide-valve  engines. 

227.  Condenser.     When  its  exhaust  pipe  opens   directly  into   the 
atmosphere,  an  engine  is  called  a  non-condensing  engine.     The  power 
depends  on  the  excess  of  the  steam  pressure  in  the  boiler  above  that 
of  the  atmosphere  outside.     Ordinary  locomotives  and  most  small 
engines  are  of  this  type.     In  fact,  the  locomotive  depends  on  the  puffs 
of  escaping  steam,  which  blow  smoke  up  the  stack  ahead  of  them,  to 
furnish  a  draft  for  the  boiler. 

Greater  economy  is  obtained  by  sending  the  exhaust  steam  to  a 
vacuum  chamber,  or  condenser.  In  one  type  the  steam  coming  from 
the  engine  is  condensed  by  a  jet  of  cold  water,  and  in  another  type  it 
is  condensed  in  a  large  steel  box  filled  with  tubes  through  which  cold 
water  is  circulated.  A  small  pump  is  used  to  pump  out  the  condensed 
steam,  as  well  as  any  air  which  may  have  leaked  in.  Such  engines  are 
known  as  condensing  engines.  Marine  engines  are  almost  always 
condensing  engines,  so  that  the  condensed  steam  can  be  put  back  into 
the  boilers,  which  would  soon  be  ruined  if  supplied  with  salt  water. 

228.  Efficiency  of  a  steam  plant.     We  have  already  seen 
that  the  modern  steam  boiler  has  an  efficiency  of  about  70  % ; 
but  there  are  still  larger  losses  in  the  engine  itself.     The  escap- 
ing steam  from  an  engine  always  carries  away  a  large  amount 
of  unutilized  heat  energy.     It  can  indeed  be  proved  that  the 
greatest  efficiency  possible  for  a  steam  engine  running  with  a 
boiler  pressure  of  163  pounds  is  only  18.5  %. 

It  must  be  remembered  that  this  18.5%  is  the  efficiency 
of  the  engine  alone,  so  that  the  efficiency  of  the  engine  and 
boiler  would  be  18.5%  of  70%,  or  only  about  13%.  This  means 


262  HEAT  ENGINES 

that  about  87%  of  the  energy  of  the  coal  would  not  be  con- 
verted into  mechanical  energy.  By  using  very  high  tempera- 
tures, the  best  engines  have  been  made  to  utilize  about  20%  of 
the  energy  originally  in  the  coal.  The  ordinary  locomotive, 
however,  does  not  utilize  more  than  8%. 

229.  Expanding  steam.     If  live  steam  from  the  boiler  is  allowed  to 
push  the  piston  through  its  entire  stroke,  and  is  then  thrown  away, 
that  is,  is  allowed  to  pass  into  the  atmosphere  or  into  a  condenser,  it 
is  evident  that  much  energy  is  wasted.     To  get  more  work  out  of  the 
steam,  the  valve  is  closed  after  the  piston  has  made  about  \  or  \  of 
its  stroke,  and  the  steam  is  allowed  to  expand  through  the  rest  of  the 
stroke.     The  pressure  and  the  temperature  of  the  steam  drop  rapidly 
after  "  cut-off." 

230.  Cylinder  condensation.    When  the  exhaust  valve  of  a  steam 
engine  opens,  there  is  a  sudden  drop  in  the  pressure  of  such  steam 
as  cannot  immediately  escape,  and  its  temperature  is  much  lowered. 
Then,  as  the  piston  returns,  this  cooler  steam  is  pushed  up  into  the 
end  of  the  cylinder  and  cools  the  metal  walls  there.     When  the  next 
charge  of  high-pressure  hot  steam  from  the  boiler  comes  in,  it  has  to 
warm  the  walls  again,  and  a  good  deal  of  steam  is  condensed  in  the 
process.     This  cylinder  condensation  is  one  of  the  important  causes 
of  inefficiency  in  steam  engines. 

231.  Compound    engines.     Cylinder    condensation    can    be    much 
reduced  by  using  the  steam  first  in  a  small  high-pressure  cylinder 
with  a  small  drop  in  pressure ;  the  exhaust  from  this  cylinder  is  then 
passed  into  a  larger  intermediate-pressure  cylinder,  where  it  undergoes 
another  small  drop  in  pressure  ;  the  steam  finally  passes  to  a  third  low- 
pressure  cylinder,  where  a  third  small  drop  in  pressure  brings  it  down 
to  the  pressure  at  which  it  is  to  be  discharged.     In  such  an  engine, 
called   a  triple-expansion   engine,    the  range  of   temperature  in  any 
one  cylinder  is  reduced  to  about  one  third,  and  losses  due  to  cylinder 
condensation  are  much  reduced.     Sometimes  only  two  cylinders  are 
used,  and  such  an  engine  is  called  a  compound  engine ;  occasionally 
the  steam  is  used  in  four  cylinders,  one  after  the  other,  in  what  is 
called  a  quadruple-expansion  engine. 

232.  Uniflow    engine.      The   plan    in    this    very    modern    type    of 
steam  engine  is  to  make  most  of  the  cooler  steam  flow  out  of  the 
cylinder  at  the  middle.     In  other  words,  the   steam  flows  out  of  the 
cylinder  in  the  same  direction  in  which  it  enters;  hence  the  name, 
uniflow. 


UNIFLOW  ENGINE 


263 


Fig.  252.     Diagram  of  a  uniflow  steam  engine. 


Figure  252  shows  a  piston  P  nearly  half  the  length  of  the  cylinder. 
Around  the  middle  of  the  cylinder  is  a  row  of  slots  in  the  wall,  and 
at  this  point  the  cylinder  is  surrounded  by  a  ring-shaped  channel  which 
is  connected  with  the  condenser  through  the  pipe  E.  The  steam 
enters  one  end  of  the 
cylinder  through  the 
valve  B  and  pushes 
the  piston  forward. 
As  soon  as  the  piston 
uncovers  the  slots  in 
the  middle  of  the  cyl- 
inder, the  steam  es- 
capes through  these 
into  the  condenser. 
But  at  the  same  time 
the  engine  has  closed 
valve  B  and  opened 
valve  A  at  the  other  end  of  the  cylinder.  The  steam  now  pushes  the 
piston  back  again  until  it  again  uncovers  the  exhaust  slots  in  the  middle. 
Each  time  that  the  piston  starts  back,  it  traps  a  considerable  amount 
of  steam  and  compresses  it  nearly  to  boiler  pressure,  thus  helping  to 
keep  the  admission  ends  of  the  cylinder  warm. 

QUESTIONS  AND  PROBLEMS 

1.  Why  does  the  water  in  a  locomotive  not  boil  at  100°  C.  ? 

2.  Why  are  not  the  "  superheater  "   pipes  in  figure  247  placed 
directly  over  or  beside  the  fire  itself  ? 

3.  The  area  of  the  piston  of  a  steam  engine  is  120  square  inches 
and  its  stroke  is  2  feet.     If  the  "  mean  effective  pressure  "  of  the  steam 
is  50  pounds  per  square  inch,  what  is  the  total  force  exerted  on  the 
piston  ? 

4.  In  problem  3,  how  many  foot  pounds  of  work  are  done  in  one 
revolution  of  the  shaft  (two  strokes)  ? 

6.  If  the  engine  in  problem  3  is  making  150  revolutions  per  minute, 
what  is  its  "  indicated  horse  power  "  ;  that  is,  what  is  the  rate  in  horse 
power  at  which  the  steam  does  work  on  the  piston? 

6.   There  is  a  well-known  formula  that  is  often  written 

2PLAN 
33000 


264 


HEAT  ENGINES 


where  P  is  the  "  mean  effective  pressure  "  in  a  cylinder,  in  pounds 
per  square  inch,  L  is  the  length  of  the  stroke  in  feet,  A  is  the  area  of 
the  piston  in  square  inches,  and  N  is  the  r.p.m. 

(a)  Of  what  quantity  does  the  formula  give  the  value  ?  Prove  your 
answer. 

(6)  Can  you  explain  why  such  a  queer  mixture  of  foot  units  and 
\nch  units  is  used  ? 


7. 


Fig. 


A  locomotive  with  cylinders  27  inches  in  diameter  and  a  stroke  of 
2.5  feet  is  provided  with  driving  wheels 
5  feet  in  diameter.  If  the  mean  effec- 
tive pressure  of  the  steam  in  the  cylinder 
is  60  pounds  per  square  inch,  and  the 
engine  is  making  50  miles  an  hour,  what 
is  the  indicated  horse  power? 

8.  How  much  mean  effective  steam 
pressure  will  be  needed  to  get  10  horse 
power  from  a  "  donkey  engine  "running 
at  200  revolutions  per  minute  ?   (Assume 
area  of  piston  to  be  50  square  inches, 
and  stroke  1  foot.) 

9.  Piston  valves  (Fig.  253)  are  now 
ordinarily  used  on  steam  engines,  espe- 
cially locomotives.     How  do  they  work  ? 


253.     Piston  valve  used  on 
modern  steam  engines. 


PRACTICAL  EXERCISE 


Running  a  steam  engine.  Examine  carefully  the  parts  of  a  small 
boiler  and  engine.  Be  sure  that  you  understand  the  use  of  each  part 
of  the  demonstration  model.  Fill  the  boiler  about  three-fourths  full  of 
water  and  heat  by  means  of  a  gas-burner  in  the  fire  box.  When  you 
have  sufficient  steam  pressure,  open  the  valve  between  the  boiler 
and  engine  and  run  the  engine.  How  would  you  determine  the 
efficiency  of  the  model  plant? 

233.  Steam  turbine.  Thus  far  we  have  been  describing 
reciprocating  engines,  in  which  the  back-and-f orth  motion  of 
the  piston  rod  is  turned  into  rotary  motion  by  means  of  a 
crank  and  connecting  rod.  Since  the  piston  must  come  to  a 
standstill  at  the  end  of  each  stroke,  this  means,  in  high-speed 
engines,  very  frequent  starting  and  stopping,  which  causes  so 
much  shaking  as  to  require  big  and  expensive  foundations. 


STEAM   TURBINES 


265 


On  steamships  the  continual  jarring  causes  a  disagreeable  vibra- 
tion. In  recent  years  a  new  and  distinctly  different  type  of 
engine,  the  steam  turbine,  has 
been  developed,  in  which  there  is 
no  reciprocating  motion. 

234.  De  Laval  steam  turbines.  In  this 
turbine  (Fig.  254)  there  are  one  or 
more  nozzles  in  which  steam  expands 
from  boiler  pressure  to  atmospheric 
pressure,  forming  a  jet  of  steam  mov- 
ing at  a  speed  of  from  35  to  45  miles  a 
minute.  There  is  also  a  wheel  provided 
with  curved  blades,  called  buckets, 
against  which  the  jets  of  steam  im- 
pinge. The  rim  speed  of  these  wheels 
is  between  15  and  20  miles  a  minute, 

and  so  the  disks  must  be  made  of  the  best  steel  and  very  carefully 
shaped  and  balanced,  and  the  buckets  must  be  very  firmly  fastened  in. 
These  wheels  rotate  very  fast,  sometimes  as  fast  as  70,000  r.  p.  m.,  so 
that  only  cream  separators  can  be  run  from  the  same  shaft.  For  other 
purposes  large  reduction  gears  (Fig.  255)  are  used. 


Fig.  254.     De  Laval  steam  turbine 
with  one  set  of  nozzles. 


Fig.  255.     De  Laval  reduction  gears,  ratio  10  to  i. 


266 


HEAT  ENGINES 


$ 


STEAM   TURBINES 


267 


235.  Curtis  turbines.  These  turbines  are  made  to  run  at  lower 
speeds  by  mounting  from  2  to  40  separate  turbine  wheels  in  little  boxes 
or  cells,  each  with  its  own  set  of  nozzles,  on  a  single  shaft.  The  steam 
from  the  boiler  flows  through  all  these  boxes,  or  stages,  one  after  the 
other ;  in  each  stage  there  is  only  a  small  drop  in  pressure,  and  the 
steam  jets  have  much  lower  speeds  than  in  a  De  Laval  turbine,  thus 
permitting  much  lower  wheel-speeds. 

Sometimes,  as  in  the  older  Curtis  turbines,  each  jet  has  two  or  three 
chances  at  a  given  wheel.  After  its  first  passage  through  a  row  of 
buckets  it  escapes  with  a  velocity  which,  although  smaller  than  in  the 


Fig.  257.    Westinghouse  steam  turbine  (Parsons  type)  with  the  upper  half  of  its 

casing  lifted. 

nozzles,  is  still  high ;  the  stream  of  steam  is  then  picked  up  by  some 
stationary  blades  attached  to  the  casing,  turned  around,  and  made  to 
impinge  again  either  on  the  same  set  of  buckets,  or  on  another  row  of 
buckets  attached  to  the  rim  of  the  same  wheel  (Fig.  256). 

236.  Parsons  turbines.     In  this  turbine   (Fig.  257)  not  all    of  the 
drop  in  pressure  in  a  given  stage  occurs  in  the  nozzles.     Enough  drop 


268 


HEAT  ENGINES 


Fig.  258.  Lawn  sprinkler  illus- 
trates the  reaction  type  of  steam 
turbine. 


does  occur,  however,  in   the   nozzles   to   shoot   the   steam  into  the 
rapidly  moving  buckets  without  shock ;  then  the  steam  experiences  a 

second  drop  in  pressure  in  the  buckets 
themselves,  more  velocity  is  generated, 
and  the  steam  is  shot  out  backward 
from  the  exit  side  of  the  buckets. 
This  action  tends  to  push  the  buckets 
in  the  opposite  direction,  just  as  water 
escaping  from  the  arms  of  a  lawn 
sprinkler  (Fig.  258)  pushes  the  arms 
around.  Parsons  turbines  (Fig.  259) 
commonly  have  a  great  many  rows  of 
moving  buckets,  or  blades,  sometimes 
several  hundred,  mounted  on  a  cylindri- 
cal or  cone-shaped  "  rotor  "  instead  of 
on  separate  wheels,  so  that  they  look 
quite  different  from  other  turbines  ;  but 
the  fundamental  principles  involved  are 
much  the  same  for  all  types  of  turbines. 

237.  Gas  and  oil  engines.  The  essential  difference  between 
a  steam  engine  and  a  gas  or  oil  engine  is  that  in  the  case  of  the 
steam  engine  the  fuel  is  burned  under  a  boiler  and  the  working 
substance,-  steam,  is  con- 
ducted to  the  engine  in 
pipes ;  while  in  the  case  of 
the  gas  or  oil  engine  the 
fuel  is  burned  in  the  cylin- 
der of  the  engine  itself  and 
the  hot  products  of  -com- 
bustion are  themselves  the 
working  substance.  In  other  words,  the  gas  engine  is  an 
internal-combustion  engine. 

The  first  engines  of  this  type  used  ordinary  illuminating  gas 
for  fuel ;  this  is  the  origin  of  the  name  "  gas  engine."  Now- 
adays liquid  fuels  are  chiefly  used,  particularly  gasoline  in 
automobiles  and  motor  boats,  kerosene  in  farm  tractors,  and 
sometimes  crude  oil  or  -even  fuel  oil  (i.e.  crude  oil  from  which 
the  gasoline  and  kerosene  have  been  removed)  in  the  modern 


Balancing  Dummies 


Rotating  Blades        Exhaust 

Fig.  259.     Diagram  of  a  Parsons  turbine. 


GAS  AND  OIL  ENGINES 


269 


270 


HEAT  ENGINES 


oil  engine.  Some  true  gas  engines  are  still  in  use,  running  on 
producer  gas  made  from  coal,  or  on  the  gas  produced  by  blast 
furnaces  (Fig.  260). 

238.  The  carburetor.     This  is  a  device  for  changing  a  liquid  fuel, 
such  as  gasoline  or  kerosene,  into  a  vapor  and  mixing  it  with  air  in  the 


Gasoline  Regulating 
Needle  Valve 


Throttle  Levei 


Air  Current 
Air  Intake  Valve 


Throttle  Valve 

Go&oline  Vapor 

and  Air 
Cork  Float 


Drain  Cock 


Fig.  261.     Section  through  a  puddle  type  of  carburetor. 

proper  proportion  for  complete  combustion.  Probably  the  simplest 
type  of  carburetor  is  the  one  shown  in  figure  261.  Here  a  shallow  pool 
of  gasoline  forms  in  the  bottom  of  the  U-shaped  air  passage,  and 

when  just  the  right  amount  has  flowed 
in,  the  needle  valve  is  closed  by  the 
rising  of  the  float.  Then  a  puff  of  air 
is  drawn  over  the  surface  of  the  pool 
and  picks  up  the  gasoline  partly  as 
vapor  and  partly  as  spray. 

Most  modern  carburetors  are  of  the 
spray  or  nozzle  type,  in  which  a  jet 
of  gasoline  is  sprayed  into  a  current 
of  air  to  form  an  explosive  mixture. 
Figure  262  shows  the  principle  of  the 
spray  carburetor.  The  commercial 

carburetor  of  to-day  has  to  vaporize 

Fig.  262.    Diagram  illustrating  pnn-    ,  ,    ,.,      ,.      .,      ,,          ,,  * 

ciple  of  jet  type  of  carburetor.         less    volatile    liquids    than  formerly, 

has  to  operate  in  winter  as  well  as  in 

summer,  and  has  to  provide  the  proper  mixture  for  high  speeds  as 
well  as  for  low  speeds.  For  these  reasons  the  modern  carburetor  is  a 
delicate  and  complicated  piece  of  mechanism. 


HOW   THE  GAS  ENGINE   WORKS 


271 


239.  Cooling  the  gas  engine.  Since  the  cylinder  of  the 
gas  engine  has  to  be  a  furnace  as  well  as  a  cylinder,  it  would  get 
dangerously  hot  if  it  were  not  cooled  from  the  outside.  It 
may  be  water-cooled  by  surrounding  it  with  a  jacket  in  which 
water  is  circulated.  Figure  216  shows  the  convection  currents 
of  water  in  the  cooling  system  of  an  automobile.  The  water 
heated  in  the  cylinder  jackets  rises  and  flows  over  into  the 
top  part  of  the  radiator,  where  it  is  cooled.  It  is  then  carried 
back  from  the  lower  portion  of  the  radiator  to  the  engine  cylin- 


Fig.  263.     Air-cooled  automobile  engine. 

der.  In  many  automobiles  this  natural  convection  current  is 
helped  by  a  centrifugal  pump,  and  in  this  case  a  lighter  radiator 
and  less  water  may  be  used  than  in  the  convection  system. 

It  is  possible  to  have  the  cylinders  of  a  gas  engine  air-cooled 
by  giving  them  a  corrugated  outer  surface  which  radiates  heat 
rapidly,  and  by  forcing  a  stream  of  air  over  this  surface.  This 
system  of  cooling  is  used  on  motor  cycles,  on  a  few  automobiles 
(Fig.  263),  and  on  rotary  airplane  engines. 

240.  How  the  gas  engine  works.  Nearly  all  gas  engines 
are  driven  by  explosions  which  take  place  within  the  cylinder  of 
the  engine  and  drive  the  piston,  this  motion  being  transmitted 


272 


HEAT  ENGINES 


through  the  connecting  rod  to  the  crank  shaft.  These  explosions 
are  quite  like  the  explosion  of  gunpowder  in  a  gun.  A  mixture 
of  gas  and  air  is  taken  into  the  closed  end  of  the  cylinder  and 

then  ignited ;  the  explosion  is  an 
almost  instantaneous  combustion, 
producing  a  very  high  temperature 
and  a  corresponding  increase  in 
pressure. 

We  may  illustrate  the  explosive  force 
of  a  mixture  of  gas  and  air  by  pouring 
a  few  drops  of  gasoline  into  an  empty  tin 
can.  (The  amount  to  be  used  depends 
on  the  size  of  the  can  and  may  be  de- 
termined by  trial.)  An  ordinary  auto- 
mobile spark  plug  is  inserted  in  the  side 
of  the  can  (Fig.  264),  which  is  then  cov- 


Fig.  264.  Exploding  a  mixture 
of  gasoline  vapor  and  air  with 
an  electric  spark. 


ered  and  shaken  in  order  to  vaporize  the  gasoline  and  mix  it  with  air. 
A  spark  is  then  made  to  pass  between  the  plug  terminals  by  means  of 
an  induction  coil.  If  there  is  the  proper  proportion  of  gas  and  air  in 
the  can,  there  will  be  an  explosion  which  will  blow  off  the  cover. 

After  the  explosion  of  the  gases  in  an  engine,  the  products  of 
combustion  must  be  got  rid  of  and  a  fresh  charge  of  gas  and 
air  must  be  taken  in  for  the  next  explosion.  There  are  two  ways 
of  performing  this  operation.  One  is  used  in  four-stroke  engines, 
which  have  an  explosion  once  in  four  strokes  or  two  revolutions, 
and  the  other,  in  two-stroke  engines,  which  have  an  explosion 
once  in  two  strokes  or  one  revolution. 

241.  The  four-stroke  engine.  This  is  the  form  most  com- 
monly used  for  automobiles  and  for  stationary  engines.  There 
are  two  valves  in  the  end  of  the  cylinder  (Fig.  265) :  an  inlet 
valve  A,  which  admits  the  mixture  of  gas  and  air  from  the 
carburetor ;  and  the  exhaust  valve  B,  which  opens  into  an 
exhaust  manifold,  from  which  the  spent  gases  are  discharged 
through  a  muffler  (or  silencer)  into  the  atmosphere.  A  spark- 
plug is  inserted  in  the  closed  end  of  the  cylinder  for  the  igni- 
tion of  the  mixture. 


THE  FOUR-STROKE  ENGINE 


273 


(c) 


(d) 


F<>^  strokes  of  a  gas  engine  :  (a)  suction 


(b)   compression,    (c) 
(d)  exhaust  stroke 


explosion  or  working,  and 


The  engine  works  in  the  following  way.     On  the  first  stroke,  called  the 
suction  stroke  (Fig.  265  (a)),  the  inlet  valve  is  open  and,  as  the  piston 
descends,  a  fresh  charge 
of  gas  and  air  is  drawn          A  B  A 

in.  On  the  next  stroke, 
called  the  compression 
stroke  (Fig.  265  (6)), 
the  piston  rises  with 
both  valves  closed  and 
the  gas  is  compressed 
to  from  -J  to  i  of  its 
original  volume.  Just 
as  the  piston  gets  to  the 

top,    the  ignition    sys- 

, 

tern,  under  the  control 

of  a  "  timer,"  shoots  a 
spark  across  the  gap  of  the  spark  plug  and  an  explosion  takes  place. 
The  piston  is  pushed  down  by  the  high  pressure  exerted  by  the  very 
hot  gases  expanding  behind  it.  This  is  called  the  expansion  or  working 
stroke  (Fig.  265  (c)).  Just  as  the  piston  reaches  the  bottom  the 
exhaust  valve  is  opened,  and  the  burned  gases  are  forced  out  while 
the  piston  moves  up.  This  is  the  exhaust  stroke  (Fig.  265  (d)). 

The  four  strokes  are,  then,  (1)  suction  stroke,  (2)  compression 
stroke,  (3)  working  stroke,  and  (4)  exhaust  stroke.  These  four 
strokes  constitute  one  complete  cycle  or  round  of  action.  The 
whole  cycle  requires  2  whole  revolutions  of  the  crank  shaft 
for  its  completion.  Since  power  is  obtained  only  on  every 
alternate  outward  stroke,  a  heavy  flywheel  is  used  to  keep  the 
engine  going  during  the  other  3  strokes.  In  automobile  and 
airplane  engines,  4,  6,  8,  or  12  cylinders  are  used  to  drive  a 
single  crank  shaft,  and  are  so  timed  that  one  or  the  other  of  them 
is  delivering  power  all  the  time  (Fig.  266). 

242.  The  two-stroke  engine.  This  form  of  engine  (Fig.  267) 
is  often  used  on  motor  boats.  The  explosive  mixture  is 
taken  into  an  air-tight  crank  case  and  slightly  compressed  on 
the  downstroke  of  the  piston.  As  the  piston  nears  the  bottom 
of  its  stroke,  it  uncovers  first  the  exhaust  port  E,  letting  part 
of  the  spent  gases  in  the  cylinder  blow  off,  and  then  the  trans- 


274 


HEAT  ENGINES 


fer  port  B.  The  slightly  compressed  charge  in  the  crank  case 
then  rushes  into  the  cylinder,  sweeping  out  the  rest  of  the 
exploded  gases  before  it.  On  the  upstroke  of  the  piston  the 
ports  are  covered  and  the  fresh  charge  is  compressed.  As  the 


Fig.  266.  A  four-cylinder  automobile  engine  partly  cut  away  to  show  pistons  P, 
valves  VV,  spark  plug  S,  crank  shaft  C,  connecting  rod  CR,  cam  shaft  CS, 
water  jacket  W,  oil  pump  OP,  and  flywheel  F. 

piston  passes  its  upper  dead  center  (or  soon  afterward),  the 
charge  is  exploded.  The  only  true  valve  in  this  engine  is  a 
light  check  valve,  where  the  fresh  gases  enter  the  crank  case. 
The  disadvantage  of  this  type  of  engine  is  that  some  of  the 
fresh  gas  is  lost  with  the  spent  gases  through  the  exhaust,  so 
that  it  uses  more  gasoline  than  some  other  types.  But,  on 
the  other  hand,  it  is  very  simple  and  gives  a  push  every  revo- 
lution. 


OIL  ENGINES 


275 


243.  Control  of  gasoline  engines.  The  power  delivered  by  a  gas 
engine  can  be  varied  within  wide  limits  by  means  of  a  throttle. 
This  valve  is  usually  of  the  butterfly  type  (much  like  a  damper  in  a 
stove  pipe),  and  is  placed  in  the  outlet  pipe  of  the  carburetor  so  as  to 
change  the  amount  of  mix- 
ture that  the  engine  receives 
during  each  suction  stroke. 

A  second  way  of  chang- 
ing the  power  is  by  varying 
the  time  of  the  explosion. 
If  the  explosion  does  not 
come  at  the  upper  dead 
center,  but  part  way  down 
the  expansion,  or  working, 
stroke,  the  power  yielded  is 
much  less.  This  is  done  to 
make  an  engine  run  slowly. 

Adjusting  the  electrical  con-  Fig  26?  .    Two.stroke  gas  engine. 

nections  so  as  to  bring  the 

time  of  explosion  nearer  the  upper  dead  center  is  called  advancing  the 
spark.  Running  on  a  "  retarded  spark  "  wastes  gasoline,  because 
the  amount  used  per  stroke  is  the  same  as  at  full  power.  The  greatest 
economy  of  fuel  will  result  when  the  engine  is  driven  with  as  little 
throttle  opening  as  possible  and  with  the  greatest  spark  advance 
the  motor  speed  will  allow. 


PRACTICAL  EXERCISE 

Ford  engine.  Study  the  construction  and  operation  of  the  Ford 
engine  as  outlined  in  Good's  Laboratory  Projects  in  Physics  (Mac- 
millan).  If  your  school  laboratory  does  not  have  such  an  engine  for 
demonstration,  visit  an  automobile  repair  shop. 

244.  Oil  engines.  Almost  any  gasoline  engine  will  operate 
for  a  time  on  kerosene,  provided  it  has  been  started  and  thor- 
oughly warmed  up  on  gasoline.  But  the  engine  will  not  be 
likely  to  run  very  long  unless  the  carburetor  is  specially  designed 
for  this  less  easily  vaporized  fuel.  However,  kerosene  engines 
are  now  successfully  used  on  many  farm  tractors  (Fig.  268). 

When  crude  oil  is  used  as  a  fuel,  pure  air  is  drawn  into  the 
cylinder,  rapidly  compressed,  and  thereby  greatly  heated. 


276 


HEAT  ENGINES 


Then  the  fuel  is  sprayed  directly  into  the  cylinder.  In  the 
Diesel  engine  (Fig.  269)  the  oil  is  blown  in  by  an  auxiliary 
stream  of  highly  compressed  air.  In  another  type  of  oil 
engine  (Fig.  270),  the  fuel  is  pushed  out  of  a  little  cup  in  the 
cylinder  by  the  explosion  of  some  air  from  the  cylinder  itself ; 
this  air  is  trapped  while  being  compressed,  and  blows  out 
again  as  soon  as  the  piston  begins  to  move  back.  Neither  the 


Fig.  268.  Farm  tractors  often  use  kerosene  as  well  as  gasoline  for  fuel.  These 
"  cross-country  locomotives  "  are  used  in  hauling  freight,  in  road  building, 
and  in  logging.  In  the  World  War  tractors  in  a  modified  form  were  used  as 
"  tanks." 

Diesel  nor  the  other  oil  engine  needs  a  carburetor  or  a  spark 
plug  because  the  oil  begins  to  burn  as  soon  as  it  comes  in  contact 
with  the  highly  compressed  hot  air.  These  engines  are  built 
in  both  4-stroke  and  2-stroke  types. 

Diesel  engines  are  used  to  drive  submarines  and  freight 
ships,  because  they  are  economical  in  the  use  of  fuel,  need  no 
large  funnels,  and  eliminate  smoke,  cinders,  and  ashes.  How- 


MECHANICAL  EQUIVALENT  OF  HEAT 


277 


ever,  these  engines  require  a  plentiful  supply  of  compressed  air 
for  starting  and  maneuvering,  and  are  more  difficult  to  keep 
in  repair  than  steam  engines.  The  other  oil  engine  is  corn- 


Fig.  269.  Four-cylinder  Diesel  type  of  oil  engine.  This  unit  (rated  at  585  horse 
power)  supplies  power  to  a  large  flour  mill  by  means  of  a  rope  drive.  It  is 
also  direct-connected  to  an  electrical  generator. 

monly  used  for  small-power  purposes,  such  as  driving  farm 
machinery. 

245.  Mechanical  equivalent  of  heat.  We  have  been  con- 
sidering the  efficiency  of  engines  without  stopping  to  describe 
how  it  is  measured.  Evidently  we  must  have  some  way  of 
comparing  the  output,  which  would  naturally  be  measured  in 
foot  pounds  or  kilogram  meters,  with  the  input,  which  would 
naturally  be  measured  in  B.t.u.  or  calories.  This  involves 
finding  a  definite  relation  between  a  foot  pound  and  a  B.t.u., 


278 


HEAT  ENGINES 


Fig.  270.     Section  'of  the  "cylinder  of  a 
injection"  oil  engine. 


or  between  a  kilogram  meter  and  a  calorie.  This  problem  was 
not  solved  until  about  the  middle  of  the  last  century,  when  an 
f  Englishman,  Joule,  did 

his  famous  experiment  of 
churning  water. 

He  arranged  a  paddle 
wheel  in  a  box  of  water 
(Fig.  271).  The  paddles 
were  turned  by  weights 
which  descended  and  thus 
unwound  cords  on  the 
spindle  of  the  wheel. 
The  water  was  kept  from 
solid-  f0nowing  the  rotating 
paddles  by  fixed  paddles 
which  projected  from  the  sides  of  the  box. 

In  this  experiment  the  mechanical  work  put  in  could  be 
measured  by  multiplying  the  weights  by  the  distance  through 
which  they  fell ;  and  the  heat  produced  could  be  measured  by 
multiplying  the  weight  of  the 
water  by  the  rise  in  tempera- 
ture. Great  care  was  taken 
to  prevent  any  loss  of  heat. 
The  result  of  this  and  many 
other  experiments  of  a  similar 
nature  led  Joule  to  announce 
the  principle :  The  number  of 
units  of  work  put  in  is  always 
proportional  to  the  number  of 
units  of  heat  produced. 

As  a  result  of  Joule's  experiments,  of  the  more  accurate 
experiments  of  Rowland  in  Baltimore,  Md.,  and  of  many 
others,  it  appears  that  778  foot  pounds  of  work  are  equivalent 
to  the  heat  required  to  raise  one  pound  of  water  one  degree  Fahren- 
heit, or  that  the  energy  required  to  heat  one  kilogram  of  water  one 


Fig.  271.     Joule's  machine  for  measuring 
the  mechanical  equivalent  of  heat. 


PROBLEMS  279 

degree  centigrade  is  equal  to  the  work  done  in  raising  one  kilogram 
to  a  height  of  427  meters. 

1  B.t.u.  =  778  foot  pounds  of  work. 
1  kilogram  calorie  =  427  kilogram  meters  of  work. 

To  compute  the  efficiency  of  an  engine  we  have,  therefore, 
to  divide  the  work  done  by  the  heat  put  in,  expressing  both  in 
the  same  units  by  means  of  the  above  relationships. 

This  work  of  Joule's  was  a  decisive  argument  in  favor  of 
the  principle  of  the  conservation  of  energy,  for  it  meant  that 
heat  and  work  are  but  different  forms  of  energy. 

PROBLEMS 

1.  The  Falls  of  Niagara  on  the  American  side  are  about  165  feet 
high.     If  no  energy  were  lost  by  radiation  by  the  water  on  the  way 
down,  or  turned  into  latent  heat  by  the  evaporation  of  spray,  how 
much  warmer  would  the  water  be  in  the  river  below  the  falls  than  at 
the  top?     (Hint:   Consider  1  pound  of  water.) 

2.  If  a  horse  power  is  equal  to  33,000  foot  pounds  of  work  per 
minute,  how  many  foot  pounds  are  there  in  a  horse-power  hour ;   that 
is,  in  the  total  amount  of  work  produced  by  a  1-horse-power  engine 
working  for  one  hour  ? 

3.  A  pound  of  average  coal  yields  14,000  B.t.u.  when  burned.     To 
how  many  foot  pounds  is  this  heat  equivalent  ? 

4.  From  the  results  of  problems  2  and  3,  calculate  the  horse-power 
hours  per  pound  of  coal  if  all  the  heat  energy  could  be  turned  into  work. 

5.  A  test  of  a  certain  steam  engine  showed  that  1  pound  of  coal 
generated  1  horse-power  hour ;  from  the  three  preceding  problems  com- 
pute the  efficiency. 

6.  The  overall  efficiency  of  a  certain  steam  plant  is  15%,  and  it 
runs  steadily  for  7\  hours  each  day  delivering  2334  horse  power.    How 
many  tons  of  coal  must  be  burned  per  day? 

7.  If  a  ton  of  coal  costs  $7.00,  what  does  the  fuel  cost  to  run  for 
one  hour  a  1556- horse-power  locomotive  whose  efficiency  is  8%? 

8.  If  a  gallon  of  gasoline  yields  110,000  B.t.u.  when  burned,  and 
the  efficiency  of  an  automobile  engine  is  20%,  how  many  horse-power 
hours  will  a  gallon  produce? 

9.  If  an  automobile  can  average  20  miles  per  gallon  of  gasoline-!^ 
at  24  miles  an  hour  with  an  engine  the  average  output  of  which  is 
10  horse  power,  what  is  the  overall  efficiency  of  the  car? 


280 


HEAT  ENGINES 


SUMMARY  OF  PRINCIPLES  IN  CHAPTER  XII 

The  mechanical  equivalent  of  heat  is  the  value  in  foot  pounds 
of  one  B.t.u.  or  in  kilogram  meters  of  one  calorie. 

1  B.t.u.  =  778  ft.  Ibs. 
1  kg.  cal.  =  427  kg.  meters. 

Efficiency  =  ?«*E»t 
input 

Both  must  be  expressed  in  the  same  unit. 


QUESTIONS 

1.  Why  does  a  steam  jacket  increase  the  efficiency  of  a  steam 
engine  ? 

2.  Does  a  water  jacket  increase  the  efficiency  of  a  gasoline  engine  ? 

3.  How  are    the   cylin- 
ders of  engines  lubricated  ? 

4.  How     does    a     ship 


Transmission  Spline  Shaft 
Second  Speed  Gear 


equipped  with  steam  tur- 
bines reverse  its  propellers? 
6.  Is  an  ordinary  gas 
engine  self-starting  ?  How 
are  automobile  engines 
made  self -starting  ? 

6.  Why  is  a  system  of 
gears,  known  as  the  trans- 
mission (Fig.  272),  used  in 
an  automobile  to  connect 
the    crank    shaft    of    the 
engine   with    the    driving 
shaft  ? 

7.  How  would  you  com- 
pute the  efficiency  of  a  gun 
regarded  as  a  heat  engine  ? 

8.  Why  does  a  high-speed  turbine  give  more  power  than  a  low- 
speed  reciprocating  engine  of  about  the  same  size? 

9.  What  is  the  use  of  the  radiator  on  an  automobile?     Describe 
its  construction. 


Countershaft 


Countershaft 
Gear 


tntershaft 
Low  Speed  Gear 
Coun  ters  haft 
Second  Speed  Gear 


Fig.  272. 


Transmission  gears  used  on  an  auto- 
mobile. 


CHAPTER  XIII 

MAGNETISM 

The  lodestone  —  magnetic  poles  —  attraction  and  repulsion 
—  the  compass  and  the  magnetism  of  the  earth  —  magnetic 
field  —  induced  magnetism  —  permeability  —  uses  of  perma- 
nent magnets  —  theory  of  magnetism. 

246.  The  lodestone.  For  many  centuries  it  has  been  known 
that  a  certain  kind  of  rock,  called  the  lodestone,  has  the  power 
of  attracting  iron  filings  and  small  fragments  of  the  same  rock. 
Its  abundance  near  Magnesia  in  Asia  Minor  led 
the  Greeks  to  call  it  "  magnetite  "  or  "  mag- 
netic "  iron  ore. 

We  may  take  a  piece  of  magnetite  (Fe3O4)  and 
show  that  it  picks  up  pieces  of  iron  (Fig.  273),  but 
does  not  pick  up  copper  or  zinc.  We  can  magnetize 
a  knitting  needle  by  stroking  it  with  a  piece  of  mag- 
netite. 

This  kind  of  iron  ore  occurs  in  many  places  in 
this  country  as  well  as  in  Norway  and  Sweden.  Fig.  273.  Lode- 


When  a  steel  bar  is  rubbed  with  such  a  nat-  attl 


ural  magnet,  the  steel  itself  becomes  magnetic 

and  is  then  called  an  artificial  magnet.     In  a  later  chapter  we 

shall  learn  how  to  make  magnets  by  using  an  electric  current. 

247.  Magnetic  poles.  It  was  a  good  many  years  before 
anyone  in  Europe  noticed  that  the  magnetic  property  of  a 
lodestone  is  concentrated  more  or  less  definitely  in  two  or 
more  spots,  and  that  if  a  somewhat  elongated  lodestone  with 
only  two  of  these  spots,  and  those  near  its  ends,  is  hung  by  a 
thread,  it  will  set  itself  with  one  spot  toward  the  north  and 
the  other  toward  the  south.  We  now  use  magnetized  needles 

281 


282 


MAGNETISM 


instead  of  lodestones,  and  call  such  an  arrangement  a  compass 
(Fig.  274) ;  we  all  know  how  valuable  this  instrument  is  to 
mariners,  explorers,  and  surveyors.  Prob- 
ably the  Chinese  had  compasses  many  years 
before  Europeans  reinvented  them. 

The    two    spots    which    point,    one    to 
the    north    and    one    to    the    south,    are 
called  the   poles 
of   the   magnet ; 
one  is  called  the 
north-seeking 
pole  ( N)  and  the 
other  the  south- 
seeking  pole  (S) 
248.   Magnetic    repulsion.     It    was    many    centuries   after 
people  had  known  that  magnets  would  attract  things  before 
they  learned  that  magnets  sometimes  repel  things. 

If  we  bring  the  south-seeking  or  S-pole  of  a  magnet  near  the 
S-pole  of  a  suspended  magnet,  the  poles  repel  each  other  (Fig.  275). 
If  we  bring  the  two  AT-poles  together,  they  also  repel  each  other.  But 
if  we  bring  an  TV-pole  toward  the  £-pole  of  the  moving  magnet,  or  an 
£-pole  toward  the  ]V-pole,  they  attract  each  other. 


Fig.  274.     Pocket  com- 
pass. 


Fig.  275.    Like  magnetic  poles 
repel  each  other. 


That  is, 


Like  poles  repel  each  other, 
Unlike  poles  attract  each  other. 


Experiment  shows  that  these  attractive  or  repulsive  forces 
between  magnetic  poles  vary  inversely  as  the  square  of  the  distance 
between  the  poles. 

249.  Declination  and  dip.  Soon  after  the  compass  was 
invented,  it  was  noticed  that  it  did  not  point  true  north  and 
south.  For  a  long  time  it  was  supposed  that  this  deviation,  or 
declination,  was  everywhere  the  same,  until  Columbus^  on  his 
way  to  America  in  1492,  discovered  near  the  Azores  a  place  of 
no  declination.  Evidently  an  exact  knowledge  of  the  decli- 


DECLINATION  AND  DIP 


283 


nation  at  different  places  is  of  the  greatest  importance  to  mari- 
ners and  surveyors,  and  so  careful  maps  are  published  by  the 
different  governments  giving  lines  of  equal  declination.  Figure 
276  shows  such  a  map.  From  this  map  it  will  be  observed 


Fig.  277.     Needle  showing 
magnetic  dip. 


Fig.  276.     Map  showing  declination. 

that  in  the  extreme  northeastern  sec- 
tion of  the  United  States  the  decli- 
nation is  as  much  as  20°  W.  This 
decreases  to  zero  at  a  place  near  Co- 
lumbus, O.,  and  becomes  an  easterly 
declination  amounting  to  20°  E.  in 
the  northwest. 

It  was  nearly  a  hundred  years  after 
Columbus's  time  before  it  was  dis- 
covered that  if  a  compass  needle  is 
perfectly  balanced  so  that  it  can  swing 
up  and  down  as  well  as  sidewise,  its 
north-seeking  pole  will  dip  down  (Fig. 
277)  at  a  considerable  angle  in  the 


284 


MAGNETISM 


northern  hemisphere.  This  angle  increases  as  one  goes  farther 
north,  and  decreases  as  one  goes  south.  Along  a  line  near  the 
equator  there  is  no  dip.  In  the  southern  hemisphere  the  north- 
seeking  pole  of  a  needle  points  up  in  the  air,  and  Shackleton's 
South  Polar  Expedition  found  a  point  on  the  great  Antarctic 
continent  where  a  dipping  needle  would  hang  vertically  with 
its  north-seeking  pole  on  top. 

250.  The  earth  a  magnet.  An  Englishman,  Gilbert,  in  the 
sixteenth  century  was  the  first  to  explain  these  curious  magnetic 
phenomena.  He  had  ground  a  little  lodestone  into  the  shape  of 
a  globe  and  noticed  that  when  tiny  compass  needles  were 
brought  near  it,  they  acted  just  like  compasses  on  the  surface 

of  the  earth.  So  he  called 
his  lodestone  globe  the 
"terrella,"  or  "  little 
earth,"  and  came  to  be- 
lieve that  it  gave  a  true 
representation  of  the  earth 
itself. 

The  earth  is,  then,  sim- 
ply a  huge  magnet  (Fig. 
278),  much  thicker  in 
proportion  to  its  length 
than  the  magnets  with 
which  we  are  familiar  in 
laboratories,  but  other- 
wise exactly  like  them. 
It  has  a  north-seeking 
and  a  south-seeking  pole  like  any  other  magnet ;  but  from  the 
laws  of  attraction  and  repulsion  we  see  that,  curiously  enough, 
its  south-seeking  pole  must  be  at  Peary's  end,  and  its  north- 
seeking  pole  at  Amundsen's  end.  These  magnetic  poles  are 
not  exactly  at  the  geographical  poles.  One  of  them  is  in  North 
America  near  Hudson's  Bay  and  the  other  is  nearly  opposite 
in  Antarctica  near  South  Victoria  Land. 


Y 


Magnetic  Pole 
\ 


Fig.  278.    The  earth  acts  as  a  magnet. 


QUESTIONS 


285 


Since  the  lines  of  equal  declination  and  of  equal  dip  are  not  true 
circles,  the  magnetization  of  the  earth  must  be  somewhat  irregu- 
lar. Furthermore,  the  positions  of  its  magnetic  poles  are  known 
to  be  changing  slowly  from  year  to  year.  Why  these  things 
are  so,  and,  for  that  matter, 
why  the  earth  is  magnetized 
at  all,  is  not  yet  known. 

QUESTIONS 

1.  Does     a     magnet    ever 
have  more  than  two  poles? 

2.  In    what    direction    did 
Peary's    compass  point  when 
he  reached  the  North  pole  ? 

3.  How  far  is  the  magnetic 
pole    from     the    geographical 
North  pole? 

4.  How  can  you  tell  whether 
or  not  a  steel  rod  is  a  perma- 
nent magnet? 

6.  Why  are  knives,  files,  and 
scissors  sometimes  found  to  be 
magnetized  ? 

6.  Will   a    magnet    attract 
a  tin  can  ?     Explain. 

7.  Would  a  magnet  floating 
on  a  cork  in  a  dish  of  water  float 
toward  the  north,  as  well  as 
turn  north  and  south?     Give 
your  reasons. 

8.  How  would  you  use  a  compass  needle  to  determine  the  polarity 
of  the  end  of  a  mass  of  iron  ? 

9.  How  would  you  use  a  compass  needle  to  compare  roughly  the 
pole-strengths  of  two  magnets? 

251.  The  field  around  a  magnet.  Michael  Faraday  (Fig. 
279)  was  the  first  to  see  that  a  true  understanding  of  the  action 
of  magnets  could  be  had  only  by  studying  the  empty  space 
around  them,  as  well  as  the  magnets  themselves. 


Fig.  279.  Michael  Faraday  (1791-1867). 
Distinguished  English  physicist  and 
chemist.  Made  important  discoveries 
in  electrochemistry  and  in  electromag- 
netism. 


286  MAGNETISM 

One  way  to  do  this  is  to  lay  a  stiff  sheet  of  paper  (or  celluloid)  over 
a  magnet  and  sprinkle  iron  filings  on  it  (Fig.  280).  When  the  paper 
is  tapped  lightly  so  as  to  shake  the  filings  about  a  little,  they  arrange 
themselves  in  regular  lines  leading  from  one  pole  to  the  other.  This 
is  because  each  filing  gets  slightly  magnetized  by  the  influence  of  the 
original  magnet,  and  sets  itself  in  the  direction  in  which  a  tiny  compass 
needle  would  lie  if  it  were  at  the  same  place.  This  can  be  verified  by 


Fig.  280.     Magnetic  lines  of  force  around  a  bar  magnet  traced  by  iron  filings. 

actually  using  a  small  compass  instead  of  the  filings.     The  lines  can 
be  mapped  in  this  way,  but  it  is  not  as  quickly  done. 

In  this  way  Faraday  drew  what  he  called  lines  of  force  around 
a  magnet.  A  line  of  magnetic  force  may  be  defined  as  a  line 
which  indicates  at  its  every  point  the  direction  in  which  a  north- 
seeking  pole  is  urged  by  the  attractions  and  repulsions  of  all  the 
poles  in  the  neighborhood.  When  lines  of  force  are  thought  of 
in  this  way,  they  should  have  little  arrowheads  on  them,  pointing 
in  the  direction  of  their  journey  from  a  north-seeking  pole  to 
a  south-seeking  pole.  We  shall  find  this  conception  of  lines 
of  magnetic  force,  or  magnetic  flux,  a  convenient  way  of  remem- 
bering how  a  magnet  will  affect  other  magnets  in  its  vicinity. 

252.  Lines  of  force  like  elastic  fibers.  Faraday  himself 
thought  of  these  lines  of  force  as  having  a  much  more  real 


LINES  OF  FORCE  287 

meaning  than  this.     He  thought  of  them  as  actually  existing 
throughout  the  space  around  every  magnet,  even  when  there 
are  no  filings  to  show  them.     He  believed  that  they  represent 
a  real  state  of  strain  in  the  ether  (see  section  190),  in  which 
all  material  bodies  are  immersed.     Even  now  we  know  very  little 
about  what  the  ether  really  is.     We  know  simply  that  it  is  not 
a    kind   of   matter,    but 
something    much     more 
subtle  and  fundamental.      ^        \     /    ^,-—~~^    \ 

At  any  rate,  these  lines     .^  XN  \  ;/'",,---._  \\  /    ,--' 
of  force  of  Faraday's  act     _.__^:_^ 
as  if  they  were  stretched      c"    ,^ 

fibers  in  the  ether  which    •--  :* ~  "  '       ,-Xt /-•:-:.'-'.'_._ 

are  continually  trying  to   — -    ''\,-''  /\%\>   ._._-''/'/  \ SsC~- 
contract    and    are    thus      -*''       /    \  /    \ 

pulling  on  the  poles  at  /        \ 

their    ends.     They    also 

act  as'if  they  were  trying  Fig-  2Sl'  Lines  of  f™eeS!between  two  unlike 
to  swell  up  sidewise  as  they 

contract,  and  thus  seem  to  crowd  each  other  apart.     It  is  not 

easy  to  see  why  lines  of 
force  have  these  proper- 
/         ties  ;  but  once  the  prop- 
erties   are    assumed   (as 
rules  of  the  game),  it  is 
easy  to  reason  out  from 
•-*,/"     them  what  will  happen  in 

many  practical  cases. 
\  If  two  magnets  are  placed 

\        with  their  unlike  poles  to- 
gether   and  their    lines    of 
Fig.  282.    Lines  of  force   between  two  like    force  traced  with  iron  filings, 
P°les-  the  result  will  be  as  shown 

in  figure  281.  If  we  assume  that  the  lines  of  force  tend  to  contract,  it 
is  easy  to  see  that  two  unlike  poles  must  attract  each  other.  But 
like  poles  would  show  a  field  of  force  as  represented  in  figure  282 ; 


'  >,    !'    ...;:,    ..::::.:  ,;: 


288 


MAGNETISM 


Fig.  283. 
magnet 
induction. 


if  we  assume  that  lines  of  force  squeeze  against  each  other  sidewise, 
and  tend  to  separate,  evidently  two  like  poles  must  repel  each  other. 
This  is  not  an  explanation  of  why  these  things  happen ; 
it  is,  however,  an  easy  way  of  remembering  what  will 
happen,  and  it  will  be  useful  later  on. 

253.  Induced  magnetism.  If  we  plunge  one  end  of 
a  piece  of  unmagnetized  soft  iron  into  some  iron  filings, 
it  does  not  attract  them ;  but  if  we  bring  near  it  a  per- 
manent magnet,  as  shown  in  figure  283,  the  soft  iron  be- 
comes a  magnet  and  attracts  the  filings.  When  the 
permanent  magnet  is  removed,  the  soft  iron  loses  its 
magnetism  and  drops  the  filings. 

A  piece  of  iron  which  is  magnetized  by  being 
near  a  magnet  is  said  to  be  magnetized  by  induc- 
tion. If  the  pole  of  the  magnet  which  was  brought 
near  the  iron  was  a  north-seeking  pole,  the  induced 
bA  magnet  can  be  shown  by  a  compass  to  have  a 
TV-pole  away  from  the  magnet  and  a  $-pole  near 
the  magnet. 

Experiments  show  that  very  soft  iron  quickly  becomes  mag- 
netized by  induction  and  quickly  loses  its  magnetism  when  the 
field  is  removed.  Hardened  steel,  however,  is  magnetized 
with  difficulty,  but  retains  its  magnet- 
ism well.  For  this  reason  the  magnets 
used  in  telephones  and  magnetos  are  made 
of  hardened  steel. 

254.  Permeability.  If  a  piece  of  soft 
iron  is  placed  in  a  magnetic  field,  it*is  found 
that  all  the  lines  of  force  in  the  vicinity  tend 
to  crowd  into  the  iron. 

Thus,  figure  284  shows  the  field  around  the 
pole  pieces  of  a  permanent  magnet,  such  as  is 
used  in  a  magneto,  with  a  piece  of  soft  iron  shaped 
like  the  cross  section  of  the  armature  between    Fig.  284.    Field   about 
the  poles  of  the  magnet.     A  piece  of  wood  or  of  poles  of 

brass  would    have    almost    no    effect    on    the 

armaiure    core 

field.  tween  the  poles. 


USES  OF  PERMANENT   MAGNETS  289 

Lord  Kelvin  called  the  ease  with  which  lines  of  force  may 
be  established  in  any  medium,  as  compared  with  a  vacuum, 
the  permeability  of  the  medium.  Thus  iron  has  a  permeability 
several  hundred  times  greater  than  air.  When  a  watch  is 
brought  near  a  powerful  magnet,  its  balance  wheel  is  often 
magnetized.  This  disturbs  its  working.  To  protect  it  from 
such  magnetic  disturbances  a  good  watch  is  often  shielded  by 
being  inclosed  in  a  soft-iron  case.  ^ 

255.  Uses  of  permanent  magnets.    Besides  being  used  in 
mariners'    and   surveyors'   com- 
passes, magnets,  as  we  shall  learn 
in   later  chapters,  are  essential 

parts  of  various  electrical  meas-  jp^^lP^Pi^^lfFiy  wheel 
uring  instruments,  such  as  gal- 
vanometers, ammeters,  voltme- 
ters, and  watt-hour  meters. 
Every  telephone  receiver  has  a 
little  permanent  magnet  inside 
its  case.  Every  time  a  telephone  Fig.  285.  Sixteen  horseshoe  mag- 
bell  rings,  a  permanent  magnet  £*  ££  »  *«  flywheel  of  a 
has  played  its  part  in  controlling 

the  motion  of  the  clapper ;  and  on  most  rural  lines  the  current 
with  which  one  rings  up  "central"  is  generated  with  the  help 
of  several  permanent  magnets.  Every  Ford  automobile  has  16 
permanent  magnets  bolted  to  its  flywheel  (Fig.  285) ;  and  every 
motor  cycle  and  airplane  carries  permanent  magnets  in  its 
magneto.  Probably  there  are  at  least  two  hundred  million  per- 
manent magnets  in  commercial  use  in  this  country  at  the 
present  time. 

In  all  these  commercial  applications  of  the  permanent  magnet 
the  steel  is  bent  more  or  less  into  a  horseshoe  shape,  so  that 
the  two  poles  are  brought  close  together,  thereby  greatly  in- 
creasing the  strength  of  the  magnetic  field.  To  get  a  magnet 
of  constant  strength,  crucible  tungsten  steel  is  used,  and  after 
it  has  been  shaped,  hardened,  and  magnetized,  it  is  artificially 


290  MAGNETISM 

aged.     One  way  of  doing  this  is  to  heat  the  magnet  in  a  bath 
of  boiling  water  or  oil  several  times. 

256.  Theory  of  magnetism.  Our  present  theory  of  magnet- 
ism is  suggested  by  the  following  experiment. 

Let  us  harden  a  knitting  needle  or  a  piece  of  watch  spring  by  first 
heating  it  red  hot  and  then  plunging  it  into  cold  water.  Then  let  us 
magnetize  it  and  mark  the  N-pole.  If  we  now  break  it  near  the  middle 
where  it  does  not  show  any  magnetism,  we  find,  by  bringing  the  broken 
enfls  near  a  compass  needle,  that  we  have  an  JV-pole  and  an  £-pole 


N      S  i N      S     N      S     ^    N 

Fig.  286.     A  broken  magnet  shows  poles  at  the  break. 

at  the  break.     If  we  repeat  the  process,  we  find  that  each  time  the 
magnet  is  broken,  new  poles  are  formed,  as  indicated  in  figure  286. 

A  magnet  can  be  broken  into  a  great  number  of  little  mag- 
nets. A  glass  tube  full  of  iron  filings  can  be  magnetized,  but 
when  shaken,  it  loses  its  magnetism.  Any  magnet  loses  a  part 
or  all  of  its  power  if  it  is  heated  red  hot,  jarred,  hammered,  or 
twisted. 

All  these  facts  point  to  a  molecular  theory  of  magnetism, 
which  was  suggested  by  a  Frenchman,  Ampere,  and  elaborated 
by  a  German,  Weber,  and  an  Englishman,  Ewing.  Every 
molecule  of  a  bar  of  iron  is  supposed  to  be  itself  a  tiny  per- 
manent magnet  —  why,  no  one  yet  knows.  Ordinarily,  these 
molecular  magnets  are  turned  helter-skelter  throughout  the 
bar  (Fig.  287),  and  have  no  cumulative  effect  that  can  be 
noticed  outside  the  bar.  When  the  bar  is  magnetized,  how- 
ever, they  get  lined  up 
more  or  less  parallel  (Fig. 


288),  like  soldiers,  all  facing 
the    same    way.     Near   the 

Fig.  287.   Model  of  an  unmagnetized  bar.    midc*le  of   the  bar  the  front 

ends  of  one  row  are  neutral- 
ized by  the  back  ends  of  the  row  in  front ;  but  at  the  ends  of 


SUMMARY  291 

the  bar  a  lot  of  unneutralized  poles  are  exposed,  north-seeking 
at  one  end  and  south-seeking  at  the  other.  These  free  poles 
make  up  the  active  spots 
which  we  have  called  the 
poles  of  the  magnet. 

On  this  theory  it  is  easy 
to  see  that  when  a  magnet  is      Fis-  288-    Modei  of  a  magnetized  bar. 
broken  in  two  without  dis- 
turbing the   alignment    of   the   molecular   magnets,  the  n?w 
poles  which  appear  at  the  break  are   simply  collections^  of 
molecular  poles  that  have  been  there  all  the  time,  but  are  now 
for  the  first  time  in  an  independent,  recognizable  position. 
'   It  will  also  be  evident  that,  if  this  theory  is  true,  there  is  a 
perfectly  definite  limit  to  the  amount  of  magnetism  a  given 
piece  of  iron  can  have.     For  when  all  the  molecular  magnets 
are  lined  up  in  perfect  order,  there  is  nothing  more  that  can 
be  done,  no  matter  how  strong  the  magnetizing  force  may  be. 
Such  a  magnet  is  said  to  be  saturated. 


SUMMARY  OF  PRINCIPLES  IN  CHAPTER  XIII 

Like  poles  repel  each  other. 

Unlike  poles  attract  each  other. 

The  earth  is  a  magnet  with  its  south-seeking  pole  at  Peary's 
end. 

Lines  of  force  tend  to  contract  and  swell  sidewise ;  that  is, 
there  is  tension  along  them,  and  compression  at  right  angles 
to  them. 

QUESTIONS 

1.  If  two  bar  magnets  are  to  be  kept  side  by  side  in  a  box,  how 
should  they  be  arranged  ?     Why  ? 

2.  If  a  magnetic  needle  is  attracted  by  a  certain  body,  does  that 
prove  that  the  body  is  a  permanent  magnet  ? 

3.  How  must  a  ship's  compass  box  be  supported  so  as  to  remain 
steady  during  the  rolling  of  the  ship  ? 


292  MAGNETISM 

4.  One  of  the  standard  compasses  used  in  the  U.  S.  navy  is  called 
the  "  Liquid  Type."  Explain  how  it  is  constructed  and  its  advantages. 

6.  A  long  soft-iron  bar  is  standing  upright.  Why  does  its  lower  end 
repel  the  north  pole  of  a  compass  needle? 

6.  Does  hammering  the  bar  while  it  is  in  the  position  described  in 
question  5  increase  or  decrease  the  effect?     Why? 

7.  Why  are  the  hulls  of  most  iron  ships  permanently  magnetized  ? 
What  determines  the  direction  in  which  they  are  magnetized  ? 

8.  How  can  the  compass  on  an  iron  ship  be  "  compensated  "  for 
ifie  induced  magnetism  in  the  ship? 

9.  The  Carnegie  Institute  has  a  special  ship  built  almost  without 
iron.     For  what  kind  of  survey  of  the  world  do  you  suppose  it  is  made  ? 
What  is  the  advantage  of  such  a  ship  for  this  purpose? 

10.  How  does  a  jeweler  demagnetize  a  watch? 

11.  Recently  a  new  compass  has  been  developed  which  does  not 
depend  on  magnetism.     What  is  it  called?     Upon  what  principle 
does  it  work? 

12.  What  additional  information  besides  the  direction  of  the  com- 
pass is  needed  to  determine  the  true  north  ? 

PRACTICAL  EXERCISES 

1.  Making  a  magnet.     Harden  a  steel  knitting  needle,  an  old  file, 
or  a  piece  of  a  clock  spring  by  heating  it  red  hot  and  then  plunging  it 
into  cold  water.    It  may  be  magnetized  by  stroking  with  a  permanent 
magnet  or,  better  still,  by  an  electromagnet  (see  section  299).     Mount 
on  a  sewing-needle  point  in  a  little  box  and  use  as  a  compass. 

2.  Photographing  lines  of  magnetic  force.     In  a  dark  room  place 
over  a  magnet  a  piece  of  photographic  printing  paper  (Velox),  sensitized 
side  up,  so  as  to  furnish  a  flat,  horizontal  surface.     Sprinkle  iron  filings 
on  the  paper.    Turn  on  an  electric  lamp  directly  above  for  a  few  seconds, 
or  light  two  or  three  matches.     Shake  off  the  filings  and  develop  the 
paper.     Compare  your  picture  with  figure  280.     Repeat  with  two  or 
more  magnets  variously  arranged,  and  also  with  an  unmagnetized  piece 
of  soft  iron  near  a  magnet. 


CHAPTER  XIV 
STATIC,  ELECTRICITY 

Electricity  by  friction  —  conductors  and  insulators  — 
positive  and  negative  charges  —  electroscope  —  distribution 
of  electricity  —  charging  by  induction  —  condenser  —  elec- 
trophorus  —  atmospheric  electricity  —  electron  theory  of 
electricity.  ,  ". 

257.  Electricity  by  friction.     As  far  back  as  600  B.C.,  Thales, 
a  Greek,  knew  that  amber,  when  rubbed,  would  attract  bits  of 
paper  or  other  light  objects.     We  now  know  that  many  other 
substances,  such  as  rubber,  glass,  and  sulfur,  have  the  same 
property.     Anyone  can  observe  this  on  a  cold,   d^  morning 
after  combing  his  hair  vigorously  with  a  hard-rubber  comb. 
The  comb  will  then  support  long  chains  of  bits  of  paper.     Since 
amber,  in  common  with  gold  and  certain  bright  alloys,  was 
called  "  electron  "  by  the  Greeks,  these  phenomena  were  many 
years  later  named  by  Gilbert  electric  phenomena. 

Objects  which  have  gained  this  property  of  attracting  small 
bits  of  paper  are  said  to  be  electrified,  or  to  have  an  electric 
charge.  Any  object  which  has  not  been  charged  is  said  to  be 
neutral.  By  many  careful  experiments  it  has  been  found  that 
any  two  different  substances  when  rubbed  together,  or  even  brought 
into  close  contact,  become  somewhat  electrified. 

258.  Electric    vs.   magnetic   attraction.     These   electric   at- 
tractions are  in  many  ways  so  much  like  magnetic  attractions 
that  it  was  not  until  the  sixteenth  century  that  it  was  clearly 
seen  that  two  very  different  kinds  of  phenomena  are  involved. 
Magnetization  can  be  produced  only  in  three  metals,  iron,  nickel, 
and  cobalt,  and  in  one  or  two  uncommon  alloys ;  while  electri- 
fication can  be  produced  by  rubbing  almost  any  substance, 
especially  a  non-metal.     A  magnetized  body  always  has  at 

293 


294  STATIC  ELECTRICITY 

least  two  poles  where  its  magnetism  is  more  or  less  concentrated  ; 
and  these  poles  are  unlike,  for  if  one  of  them  attracts  the  north- 
seeking  end  of  a  compass,  the  other  will  always  repel  it.  A 
metallic  body  electrified  by  friction  will  ordinarily  not  have  its 
properties  concentrated  in  spots,  and  all  parts  of  it  will  act  very 
much  alike  in  their  attracting  power.  Nevertheless,  we  shall 
presently  see  that  there  are  two  kinds  of  electricity,  just  as 
there  are  two  kinds  of  magnetic  poles. 

259.  Conductors  and  insulators.  Some  substances  will 
conduct  electricity,  while  others  will  not.  Thus  a  metal  sphere 
can  be  charged  with  electricity  by  touching  it  with  some  electri- 
fied substance,  such  as  a  stick  of  sealing  wax  which  has  been 
rubbed  with  a  cat's  skin,  if  the  sphere  is  suspended  by  a  dry 
silk  thread,  but  not  if  suspended  by  a  wire.  In  the  latter 
case  just  as  much  electricity  gets  into  the  sphere  as  in  the 
former,  but  it  all  runs  out  again  through  the  wire.  Similarly 
an  electrified  body  loses  its  charge  if  touched  by  any  part  of 
the  experimenter's  body.  Substances  which  lead  off  the  electric 
charge  quickly,  such  as  metals,  are  called  conductors;  those  which 
prevent  the  charge  from  escaping,  such  as  amber  or  dry  silk, 
are  called  nonconductors  or  insulators.  It  is  to  prevent  the 
leakage  of  electricity  from  the  conductor  that  electric-light, 
telephone,  and  telegraph  wires  are  supported  on  glass  or  porce- 
lain knobs,  called  "  insulators." 

There  is  no  sharp  line  between  conductors  and  insulators ; 
most  substances  conduct  a  little,  and  even  the  good  conductors 
vary  greatly  in  conductivity. 

In  the  following  table  a  few  other  common  substances  are 
arranged  according  to  their  insulating  powers. 

INSULATORS  POOR  CONDUCTORS  GOOD  CONDUCTORS 
Hard  rubber                    Dry  wood  Metals 

Dry  air  Paper  Gas  carbon 

Paraffin  Alcohol  Graphite 

Sulfur  Kerosene  Water  solutions  of 

Resin  Pure  water  salts  and  acids 


POSITIVE  AND  NEGATIVE  ELECTRICITY          295 

It  will  be  noticed  that  the  substances  which  can  be  easily 
electrified  by  friction  are  all  insulators.     One  reason  for  this  is 
that  when  electricity  is  generated  at  any  point  on  an  insulating 
body  by  rubbing,  it  stays  there 
and  makes  its  presence  known  ; 
but  if  the  body  is  a  conductor, 
the   electricity  leaks    away   at 
once. 

Those  substances  which  are 
good  conductors  of  electricity 
are  also  good  conductors  of  heat. 
This  curious  phenomenon  seems 

to  be  due  to  the  fact  that  both   Fig.    289.     Two  electrified   rods  with 

heat  and  electricity  are  carried         like  char8es  repel  each  other, 
through  metals  by  a  swarm  of  tiny  particles,  called  electrons, 
which  drift  about  between  the  much  larger  molecules  of  metal. 

260.  Positive  and  negative  electricity.  If  we  hang  up  in  a 
stirrup,  suspended  by  a  silk  thread  (or  balance  on  a  needle  point,  sup- 
ported by  an  insulator)  a  glass  rod  which  has  been  rubbed  with  silkr 
and  then  bring  near  one  end  of  it  another  glass  rod  which  has  also  been 
rubbed,  they  repel  each  other  (Fig.  289).  In  a  similar  way,  two  hard- 
rubber  rods  or  sticks  of  sealing  wax  rubbed  with  catskin  or  flannel 
repel  each  other.  But  when  we  bring  a  rubbed  stick  of  sealing  wax 
near  a  rubbed  glass  rod  in  the  stirrup,  they  attract  each  other. 

Such  experiments  show  that  there  are  two  kinds  of  electri- 
fication. By  universal  consent  scientific  people  have  agreed  to 
call  that  kind  of  electrification  which  appears  on  glass  when 
rubbed  with  silk  positive;  and  that  kind  which  appears  on  sealing 
wax  or  hard  rubber  when  rubbed  with  flannel  negative.  Bodies 
charged  with  the  same  kind  of  electricity  repel  each  other,  and 
bodies  charged  with  different  kinds  of  electricity  attract  each 
other.  That  is, 

Like  charges  repel  and  unlike  charges  attract. 
Experiments  also  show  that  an  electrified  body,  whether  it  is 
positively  or  negatively  charged,  attracts  an  unelectrified  body. 


296 


STATIC  ELECTRICITY 


261.  How  to  detect  electricity.    To  test  the  electrical  con- 
dition of  a  body  we  use  an  electroscope.     A  simple  form  of 
electroscope  consists  of  a  pith  ball  hung  by  a 
silk  thread  from  a  glass  support  (Fig.  290). 

If  an  uncharged  body  is  brought  near  the  pith  ball, 
nothing  happens.  If  a  positively  charged  body  is 
brought  near  the  pith  ball,  the  latter  is  attracted, 
becomes  itself  positively  charged,  and  is  then  re- 
pelled. Then  if  a  negatively  charged  body  is  brought 
near,  the  positively  charged  pith  ball  is  attracted, 
but  when  it  touches,  it  becomes  negatively  charged 
and  flies  back.  If  we  now  bring  a  negatively 
Pith-ball  charged  body  near,  the  negatively  charged  pith  ball 
is  repelled.  If,  then,  we  know  what  the  nature  of 

the  charge  on  the  pith  ball  is,  and  find  that  a  body  repels  it,  we  know 

the  body  must  be  charged  the  same  way. 


Fig.  290. 

electroscope. 


A  more  reliable  form  of  electroscope  is  the  so-called  "  gold- 
leaf  "  electroscope,  although  nowadays  it  is  quite  commonly 
made  of  an  aluminum  leaf  hung  beside  a  brass  strip.  The 
instrument  is  usually  mounted  in  some  sort 
of  glass  case,  as  shown  in  figure  291,  to  protect 
it  from  air  currents. 

When  one  brings  near  the  top  of  the  brass  rod  a 
charged  glass  rod,  the  aluminum  leaf  swings  out 
from  the  brass  strip.  If  the  rod  is  removed,  the 
leaf  falls  down  again.  If,  however,  one  actually 
touches  the  charged  rod  to  the  electroscope,  the  leaf 
swings  out  and  stays  there. 

The  electroscope  is  then  said  to  be  charged  posi- 
tively. If  we  bring  near  a  positively  charged  elec- 
troscope a  positively  charged  body,  the  leaf  will  fly 
farther  out;  but  if  the  body  brought  near  has  a 
negative  charge,  the  leaf  will  swing  down.  In  either 
case  it  will  return  to  its  original  charged  position 
when  the  outside  charged  body  is  taken  away.  Thus  with  an  electro- 
scope carrying  a  known  charge  one  can  tell  the  electrical  condition 
of  a  body. 


Fig.  291.  Alumi- 
num-leaf elec- 
troscope. 


DISTRIBUTION  OF  ELECTRICITY 


297 


Fig.  292.     Charging  an  insu- 
lated tin  cup. 


With  such  an  electroscope  it  is  possible  to  learn  much  about 
electrified  bodies.  For  example,  when  an  insulated  conductor 
is  rubbed,  it  becomes  charged  with  electricity ;  so  we  conclude 
that  all  bodies  become  electrified  by  friction.  If  we  stand  on  an 
insulated  stool  while  we  rub  a  glass 
rod,  our  body  becomes  negatively 
charged;  and  by  rubbing  sealing 
wax  with  cat's  fur,  we  become  pos- 
itively charged.  In  general,  when- 
*  ever  two  different  substances  are  rubbed 
on  one  another,  one  becomes  posi- 
tively charged  with  electricity,  while 
at  the  same  time  the  other  is  nega- 
tively charged. 

262.  Distribution  of  electricity  on  a  conductor.  Let  us  place 
a  tin  cup  on  a  cake  of  paraffin,  as  shown  in  figure  292,  and  charge  it 
as  much  as  possible  either  positively  or  negatively.  We  can  then  test 
it  at  various  points  by  means  of  a  little  metal  disk  or  ball  mounted 
on  an  insulating  handle  and  known  as  a  proof  plane.  If  we  touch 
the  outside  surface  of  the  charged  cup  with  the  proof  plane  and  then 
bring  the  latter  near  the  knob  of  a  charged  electroscope,  we  find  that 
there  is  a  strong  charge  on  the  outside  of  the  cup.  If  we  touch  the 
inside  surface,  we  find  no  charge  at  all. 

That  is,  the  charge  is  entirely  on  the  outer  surface  of  a  conductor. 
It  can  also  be  shown  that  its  greatest  density  is  at  the  corners 
and  projecting  points.  In  fact,  the  density  of  the  charge  at 
sharp  points  is  so  great  that  it  will  escape  into  the  air  easily  at 
such  points. 

QUESTIONS 

1.  Compare  the  behavior  of  a  magnetic  pole  with  the  behavior  of 
an  electrically  charged  body. 

2.  Does  a  freely  swinging  charged  body  take  a  definite  direction? 

3.  What  becomes  of  the  mechanical  energy  exerted  in  rubbing  a 
glass  rod  to  electrify  it  ? 

4.  What  kind  of  electricity  is  generated  by  rubbing  a  stick  of  sulfur 
on  woolen  cloth  ? 


298 


STATIC   ELECTRICITY 


Fig.  293. 


Charging 
spheres. 


two    metal 


5.  Why  do  experiments  with  f Fictional  electricity  work  better  on  a 
cold,  dry,  winter  day? 

6.  Does  one  remove  magnetism  from  a  magnet  by  touching  it  with 
iron  ? 

7.  Faraday  built  a  large  box  and  lined  it  with  tin  foil.     He  then 
took  his  most  sensitive  electroscope  into  the  box  and  found  that  even 

when  the  outside  of  the  tin  foil  was  so 
charged  that  it  sent  forth  long  sparks, 
he  could  not  observe  any  electrical 
effects  inside.  Explain. 

8.  In  testing  the  electrification  of 
a  body  with  a  charged  pith  ball  sus- 
pended by  a  silk  thread,  would  attrac- 
tion or  repulsion  be  the  better  test? 
Why? 

9.  Which  are  more    important  in 
their  commercial  applications,  conduc- 
tors or  insulators  ?     Give  your  reasons. 

263.  Charging  by  induction.  We  have  already  seen  that 
it  is  possible  to  influence  an  uncharged  electroscope  by  bringing 
near  it  an  electrified  body ;  but  we  have  also  seen  that  this 
influence  disappears  as  soon  as  the  charged  body  is  removed. 
This  method  of  producing  a  temporary  electrification  by  the 
presence  of  a  charged  body  in  the  neighborhood  is  called  charg- 
ing by  induction. 

Let  us  illustrate  this  process  of  electrification  by  placing  two  metal 
balls  A  and  B  on  insulators 
side  by  side,  as  shown  in  figure 
293.  We  now  bring  a  nega- 
tively charged  body,  such  as  a 
rubbed  stick  of  sealing  wax, 
near  the  ball  A,  which  touches 
ball  B,  and  while  the  charged 
body  remains  near  A,  we  sep- 
arate the  balls.  On  testing  FiS-294.  Charging  a  conductor  by  induction. 

the  balls  we  find  that  A  is  positively  charged  and   B  is  negatively 
charged. 

If  a  conductor  C  is  touched  at  a  by  the  finger  while  a  negatively 
charged  rod  R  is  held  near  it,  as  shown  in  figure  294,  and  if  the  finger 


CHARGING  BY  INDUCTION  299 

is  first  removed  and  then  the  charged  rod,  we  find  that  the  conductor 
has  become  charged  positively.  If  we  repeat  the  experiment  but  this 
time  touch  the  conductor  at  some  other  point,  such  as  6,  we  find  that 
the  conductor  is  charged  positively  exactly  as  before. 

We  may  explain  this  process  of  charging  by  induction  as 
follows.  When  the  negatively  charged  rod  is  brought  near 
an  insulated  conductor,  the  pos- 
it^ive  and  negative  electricity  in 
the  conductor  are  distributed  so 
that  the  remoter  part  has  a  charge 
of  the  same  kind  as  the  inducing 
charge  and  the  nearer  part  has  a 
charge  of  the  opposite  kind.  If  we  v 
cut  the  conductor  in  two  while  it  +' 

is  under  the  influence  of  an  elec-  Fig.  295.  Charging  an  aluminum- 
trie  charge,  we  obtain  two  perma-  leaf  electrosc°Pe  b?  induction, 
nently  charged  bodies.  If  we  touch  the  conductor,  the  negative 
electricity,  which  is  repelled,  finds  its  way  to  the  ground  through 
our  body,  but  the  positive  electricity  remains  bound.  In  gen- 
eral, we  conclude  that  in  charging  by  induction  the  sign  of 
the  charge  induced  is  opposite  to  that  of  the  inducing  charge. 

This  helps  us  to  understand  the  gold-leaf  electroscope.  When 
a  charged  body  is  brought  near  the  knob  of  the  electroscope,  the 
leaf  swings  out  because  it  and  the  strip  are  charged  by  induction 
with  the  same  kind  of  electricity  as  the  charged  body  (Fig.  295) . 
If  the  electroscope  is  charged  by  contact  positively  and  a  posi- 
tively charged  body  is  brought  near,  it  repels  more  of  the  posi- 
tive electricity  into  the  leaf  and  it  swings  out  farther.  On  the 
other  hand,  if  a  negatively  charged  body  is  brought  near,  it 
draws  some  of  the  positive  electricity  up  into  the  knob,  and  the 
leaf  drops  somewhat. 

264.  Condenser.  In  many  practical  applications  of  elec- 
tricity it  has  been  found  necessary  to  increase  the  capacity  of  a 
conductor  for  holding  electricity.  This  is  done  in  what  is  called 
a  condenser. 


300 


STATIC  ELECTRICITY 


-      t 


To  earth 


Let  us  arrange  a  metal  plate  on  an  insulating  base  and  connect  the 
plate  by  a  wire  to  an  electroscope,  as  shown  in  figure  296.     If  we  charge 
the  plate  A,  we  see  the  leaf  of  the  electroscope  swing  out.     We  now 
A  R  bring  up  a  second  metal 

plate  B  similar  to  plate  A , 
but  connected  with  the 
ground.  As  we  bring 
plate  B  near  plate  A,  the 
electroscope  leaf  begins  to 
fall,  but  if  we  remove 
plate  B  again,  the  leaf 

swings  out  as  before. 
Fig.  296.     Action  of  a  condenser.  Let   us  now    bring   the 

plate  B  back  to  a  position  near  plate  A,  and  charge  plate  A  until  it 
shows  the  same  deflection  as  before.  It  will  be  evident  that  the  capac- 
ity of  plate  A  for  holding  electricity  is  much  increased  by  being  close 
to  a  similar  grounded  plate  B. 

We  may  also  show  the  influence  of  an  insulating  material  between 
the  conducting  plates  by  introducing  a  pane  of  glass.  The  leaf  of  the 
electroscope  falls,  but  rises  again  when  the  glass  is  removed.  This 
shows  that  the  capacity  of  the  condenser  is  increased  by  the  glass 
plate. 

A  combination  of  conducting  plates  separated  by  an  insulator 
is  called  a  condenser.  The  capacity  of  a  condenser  for  holding 
electricity  is  proportional  to  the  size  of  the  plates  and  increases 
as  the  distance  between  them  de- 
creases. It  also  depends  on  the  nature 
of  the  insulator,  of  dielectric,  as  it  is 
called,  being  much  greater  when  glass, 
mica,  or  paraffin  paper  is  used  than 
when  a  layer  of  air  is  the  dielectric. 

265.   Commercial  condensers.     As 
early  as  1745,  someone   at  the  Uni- 
versity of  Leyden  in  Holland  made  a    Fig.  297.     Condenser  made  in 
condenser  out  of  a  wide  jar  or  bottle        the  form  of  a  Leyden  jar' 
(Fig.  297)  by  coating  it  inside  and  out  with  tin  foil.     This 
so-called  Leyden  jar  is  still  employed  in  experimental  work. 
.But  the  condensers  used  in  telephones,  induction  coils,  and 


HYDRAULIC  ANALOGY  OF  A   CONDENSER 


301 


Foil 


Paper 


Tin  Foil 


radio  telegraphy  generally  have  a  much 

more  compact  form.    "Figure  298  shows 

two  sets  of  interlaid  layers  of  tin  foil 

separated    by    sheets   of    paper  coated 

with  paraffin,  or  by  sheets  of  mica.     The 

alternate  layers  of  tin  foil  are  connected 

to  each  other  and  form  two  terminals, 

as   shown  in  figure  299.     There  is  no          _  _ 

electrical  connection  between  the  con- 

,  ,  ,  ,      ,.  ,  .         Fig.  298.     Construction  of 

denser  terminals,  and  so  one  set  01  tin-         a  plate  condenser. 

foil  sheets   may   be  charged  positively 

while  at  the  same  time  the  other  set  is  charged  negatively. 

These  positive  and  negative  charges  hold  or  bind  each  other  so 

that  a  large  quantity  of  electricity 
may  be  accumulated.  The  capacity 
of  such  a  condenser  is  proportional 
to  the  area  of  the  plates  and  to  the 
number  in  each  set. 

Fig.  299.    Assembled  plates  of 

a  condenser.  ___     __    « 

266.  Hydraulic  analogy  of  a  condenser. 

We  may  illustrate  a  condenser  by  two  standpipes  filled  to  different 

levels  with  water,  as  shown  in  figure  300.    The  coatings  of  the  con- 

denser correspond  to  the  standpipes.     The  pipe   A,  with  the  water 

standing  at  a  higher  level,    repre- 

sents the  positively  charged  plate  or 

coating,  while  the  other  pipe  B  is 

the  negatively  charged  plate.     The 

connecting  pipe  at  the  bottom  of  the 

tanks  corresponds  to  the  wire  con- 

necting   the    coatings.      When   the 

connection  is  made,  the  water  rushes 

through  the  pipe  and  equalizes  the 

levels  very  quickly.     This  represents 

the     discharge    of    the    condenser.   Fi£-  3oo. 

When   the  valve   V  in   the  pipe  is 

first  opened,  the  water  rushes  through  so  fast  that  it  usually  over- 

does things,  and  rises  to  a  higher  level  in   B  than  in   A.     Then  it, 

flows  back  again,  and   so  on,  oscillating  back  and  forth  until  the 


Hydraulic   analogy   of  a 
condenser. 


302  STATIC  ELECTRICITY 

motion  dies  out  because  of  friction  in  the  pipe.  In  much  the.  same 
way,  when  a  condenser  is  short-circuited,  the  discharge  of  electricity 
goes  too  far  and  charges  the  condenser  the  other  way.  Then  it  dis- 
charges back  again,  and  so  the  eV  3tric  charges  oscillate  very  quickly 

back  and  forth  until  the 
motion  of  the  electricity  dies 
out  because  of  something 
akin  to  friction,  called  the 
electrical  resistance  of  the 
wire.  The  technical  way  of 
describing  this  is  to  say  that 
the  discharge  of  a  condenser 
is  oscillatory. 

267.  Induction  machines 
Fig.  301.    Electrophorus.  for    producing  electricity. 

The  simplest  machine  for  producing  electricity  by  induction  is 
the  electrophorus.  It  consists  of  a  hard-rubber  plate  and  a 
somewhat  smaller  metal  disk  with  an  insulating  handle. 

The  hard-rubber  plate  (B  in  Fig.  301)  is  rubbed  with  cat's 
fur,  which  charges  it  negatively.  We  then  place  the  metal  disk  A  on 
the  plate  and  touch  the  metal  disk  so  as  to  "  ground  "  it.  When  we 
lift  the  disk  and  bring  it  near  the  knob  of  a  Leyden  jar,  a  spark  jumps 
across  the  gap.  A  Leyden  jar  can  be  strongly  charged  with  an  elec- 
trophorus by  repeating  this  process  again  and  again. 

When  the  metal  disk  is  placed  on  the  negatively  charged  plate, 
a  positive  charge  is  attracted  to  the  lower  surface  of  the  disk  next  to 
the  plate,  while  the  negative  electricity  is  repelled.  When  we  touch 
the  metal  disk,  this  negative  electricity  escapes  through  the  hand  to 
the  ground.  By  this  process  the  disk  becomes  positively  charged 
throughout.  After  the  rubber  plate  is  once  charged,  any  number  of 
charges  can  be  obtained  from  the  electrophorus  without  producing 
any  appreciable  change  in  the  charge  on  the  plate.  This  is  because 
the  energy  comes  from  the  muscle  that  lifts  the  disk. 

There  are  more  complicated  electrostatic  machines,  such  as 
the  Toepler-Holz  and  Wimhurst  machines,  which  also  make 
use  of  the  principle  of  induction.  These  machines  are  chiefly 
used  for  lecture-table  demonstrations. 

268.   Atmospheric    electricity.     It    was    about    the    middle 


ATMOSPHERIC  ELECTRICITY 


303 


of  the  eighteenth  century  that  Benjamin  Franklin  (Fig;.  302) 
demonstrated  by  his  famous  kite  that  thunderclouds  carry 
ordinary  electrical  charges 
and  that  lightning  is  a  huge 
electrical  discharge,  or  spark. 
This  discovery  was  recog- 
nized as  epoch-making  by 
scientific  men  everywhere. 
Perhaps  the  most  wonderful 
part  of  it  was  that  Franklin 
was  not  killed  at  once,  for 
within  a  year  a  man  in  Pe- 
trograd  lost  his  life  while 
performing  a  similar  experi- 
ment. 

Franklin  then  invented 
the  lightning  rod  to  con- 
duct safely  any  electricity 

that     might     Otherwise     be  Fi«:  3°2'    Benjamin  Franklin  (1706- 1790). 

e  Famous  American  statesman,  scientist, 

discharged  through  a  build-  and  author.     Made  a  scientific  study  of 

ing   by    a    Stroke   of     light-  electricity  and  invented  the  lightning  rod. 

ning.  When  a  charged  cloud  acts  inductively  on  the  earth,  a 
bound  charge  of  opposite  sign  is  concentrated  in  good  conduc- 
tors and  outstanding  objects,  such  as  trees 
and  church  steeples  (Fig.  303),  and  we 
have  a  sort  of  huge  condenser.  If  the 
charges  become  too  great,  or  the  cloud 
comes  too  near  the  earth,  the  intervening 
dielectric  (the  air)  breaks  down  and  the 
condenser  discharges,  producing  a  flash  of 
lightning,  which  is  sometimes  five  miles 
_  _  -  long,  and  a  loud  noise  called  thunder.  The 

Fig.    303.     A  charged  sound  is  thought  to  be  caused  by  a  sud- 
ckmd  induces  an  oppo-  den  ancj  vioient  expansion  of  the  ribbon 

site  charge  in  church 

steeples.  of  air  that  is  heated  by  the  discharge. 


304  STATIC  ELECTRICITY 

Until  recently  the  cause  of  the  electrification  of  thunderclouds 
has  been  a  mystery.  It  has  now  been  shown  experimentally  that  when 
water  falls  through  an  upward  current  of  air,  violent  enough  to  produce 
spray,  the  larger  of  the  resulting  drops  are  usually  positively  electrified, 
while  the  finer  mist  carries  a  negative  charge.  Since  thunderclouds 
form  at  the  tops  of  huge  upward  currents  of  air,  it  is  clear  why  the 
heavy  rain  of  a  thunderstorm  is  usually  positively  charged,  and  why 
the  mist  which  is  swept  upward  by  the  air  current  forms  negatively 
charged  clouds. 

The  effectiveness  of  the  protection  against  lightning  afforded 
by  lightning  rods  is  a  subject  on  which  there  is  much  difference 
of  opinion.  It  is  certain  that  flimsy  rods,  poorly  erected  or  not 
well  grounded,  are  worse  than  no  rods  at  all.  On  the  other 
hand,  several  substantial  conductors  starting  from  well-distrib- 
uted points  on  a  roof  or  from  the  top  of  a  steeple  and  leading 
without  sharp  bends  and  always,  downward  to  good  grounds 
doubtless  afford  valuable  protection.  Telephone  and  electric- 
light  wires  and  electric-power  lines  are  commonly  protected  by 
various  kinds  of  lightning  arresters. 

269.  The  electron  theory  of  electricity.  We  now  believe 
that  all  substances  are  composed  of  one  or  more  simple  sub- 
stances called  elements.  Water,  for  example,  is  composed  of 
the  elements  oxygen  and  hydrogen.  We  define  an  atom  as  the 
smallest  particle  of  an  element  which  can  take  part  in  chemical 
change.  We  have  already  seen  that  a  gas  is  composed  of  a  vast 
number  of  minute  particles  called  molecules.  In  most  com- 
mon gases,  such  as  oxygen,  nitrogen,  and  hydrogen,  each 
molecule  is  made  of  two  atoms  held  together  in  chemical  com- 
bination. In  a  compound  a  molecule  is  composed  of  two  or 
more  atoms  of  different  elements.  Thus  a  water  molecule  is 
composed  of  2  atoms  of  hydrogen  and  1  atom  of  oxygen. 

The  atoms  of  all  elements  are  believed  to  contain  as  con- 
stituents both  positive  and  negative  electricity.  The  negative 
electricity  exists  in  the  form  of  very  minute  corpuscles,  or 
electrons,  which  are  grouped  in  some  way  about  the  positive 
electricity  as  a  nucleus.  Although  the  hydrogen  atom  is  the 


ELECTRON   THEORY  305 

lightest  atom  known  and  is  much  too  small  for  us  to  hope  ever 
to  see  it,  even  with  the  most  powerful  microscope,  yet  each 
electron  has  a  mass  T^4^  of  that  of  the  hydrogen  atom. 

A  negatively  charged  body  is  one  which  contains  more  electrons 
than  its  normal  number ;  a  positively  charged  body  is  one  which 
contains  less  electrons  than  its  normal  number.  In  a  conductor 
the  electrons  are  continually  getting  loose  from  the  atoms  and 
reentering  other  atoms ;  and  so  at  any  given  instant  there  are 
in  a  conductor  a  great  number  oifree  electrons  and  a  correspond- 
ing number  of  atoms  which  have  lost  electrons  and  so  are  posi- 
tively charged.  The  larger  the  number  of  free  electrons  in 
any  substance,  the  greater  the  conductivity  of  that  substance. 
An  insulator  is  a  substance  which  contains  no  free  electrons. 

The  process  of  charging  b>  induction  is  very  simply  explained 
by  the  electron  theory.  W  ^n  a  positively  charged  body  is 
brought  near  an  insulated  cone  uctor,  the  free  electrons  in  the 
conductor  are  attracted  from  all  parts  of  the  conductor  to  the 
end  nearest  the  positively  charged  body.  Hence  that  end  is 
negatively  charged.  Since  these  electrons  were  drawn  away 
from  the  far  end  of  the  conductor,  it  has  less  than  its  normal 
number  of  electrons  and  is  therefore  positively  charged. 

SUMMARY  OF  PRINCIPLES  IN  CHAPTER  XIV 

All  bodies  can  be  electrified  by  friction,  becoming  charged 
either  positively  (vitreously)  or  negatively  (resinously). 

Like  charges  repel  each  other. 

Unlike  charges  attract  each  other. 

All  conductors  can  be  electrified  by  induction,  showing  both 
a  positive  and  a  negative  charge  in  different  places.  Of  these, 
one  is  bound  by  the  inducing  charge,  but  the  other  is  free. 

QUESTIONS 

1.  Why  cannot  a  Leyden  jar  be  appreciably  charged  if  the  jar 
stands  on  a  cake  of  paraffin  ? 


306  STATIC    ELECTRICITY 

2.  If  a  charged  Leyden  jar  is  placed  on  a  cake  of  paraffin,  why  does 
one  not  get  a  shock  if  one  touches  the  knob  ? 

3.  How  would  you  with  safety  discharge  a  condenser? 

4.  Why  does  a  brick  chimney  need  a  lightning  rod  more  than  a 
steel  smokestack  of  the  same  height  ? 

6.  If  an  insulated  metal  globe  is  negatively  charged,  how  can  any 
number  of  other  insulated  metal  globes  be  positively  charged  ?  Does 
the  first  globe  lose  any  of  its  charge  ? 

6.  If  an  insulated  metal  globe  is  negatively  charged,  how  can  any 
number  of  other  insulated  metal  globes  be  negatively  charged  ?     Does 
the  first  globe  lose  any  of  its  charge  ? 

7.  In  charging  an  electroscope  by  induction,  why  must  the  finger 
be  removed  before  the  removal  of  the  charged  body? 

8.  Explain  how   the   electrophorus   illustrates   the   transformation 
of  mechanical  into' electrical  energy. 

9.  Describe  the  action  of  an  electrophorus  according  to  the  electron 
theory. 

PRACTICAL  EXERCISE 

Different  forms  of  condensers.  Find  out  how  the  condensers  in 
automobile  spark  coils  differ  in  construction  from  those  used  in  radio 
telegraphy.  Why  ? 


CHAPTER  XV 
ELECTRIC  CURRENTS 

Electricity  in  motion  —  water  currents  —  electric  cell  — 
electric  circuit  —  ampere,  ohm,  and  volt  —  hydraulic  analogy 
—  Ohm's  law  —  measurement  of  current,  voltage,  and  resist- 
ance —  computation  of  resistance  —  wire  table  —  temper- 
ature effect  on  resistance  —  series  circuits  —  Ohm's  law 
applied  to  partial  circuits  —  parallel  circuits  —  cells  in  series 
and  in  parallel  —  construction  of  a  dry  cell  —  its  defects  — 
terminal  voltage  —  voltage  drop  in  a  line. 

270.  Electricity  at  rest  and  in  motion.     Until  the  nineteenth 
century  practically  all  that  people  knew  about  electricity  dealt 
with  electricity  at  rest  (electrostatics).     Almost  the  only  use- 
ful invention  was  the  lightning  rod,  and  its  value  was  much 
overestimated.     The  most  useful  instrument  which  had  been 
devised  was  the  condenser. 

In  the  last  fifty  years,  as  we  shall  see  in  the  next  three  chapters, 
electricity  has  suddenly  leaped  into  a  commanding  position  in 
the  arts  and  in  engineering.  The  telephone,  electric  light  and 
electric  motor,  trolley  cars,  radio  telegraphy,  and  electric  trans- 
mission of  power  have  become  everyday  affairs.  All  these  in- 
volve electricity  in  motion,  that  is,  electric  currents. 

271.  Electric  currents  and  water  currents.    Although  the 
exact  nature  of  electricity,  which  makes  itself  evident  in  so  many 
ways,  has  never  been  determined,  we  can  become  familiar  with 
the  laws  governing  the  effects  and  the  applications  of  electric 
currents.     We  shall  find  it  very  useful  to  remember  that  we 
are  dealing  with  something  flowing  along  a  conductor  very  much 
as  water  flows  through  a  pipe. 

For  example,  suppose  a  water  tank  is  mounted  beside  a 
railroad  track  for  filling  the  tank  of  a  locomotive  tender,  as 

307 


308 


ELECTRIC   CURRENTS 


shown  in  figure  304.     We  know  that  the  water  will  flow  from 
the  tank  through  the  pipe  out  into  the  tender.     The  water  flows 


Fig.  304.     Difference  of  level  tends  to  make  water  flow. 

"  downhill  " ;  that  is,  it  moves  because  a  difference  in  level 
furnishes  a  motive  force  called  hydraulic  head.  This  head  is 
measured  by  the  difference  of  level  between  the  water  surface 

in  the  tank  and  the  end  of  the  pipe. 
In  much  the  same  way,  if  we 
connect  the  binding  posts,  or  ter- 
minals, of  a  dry  cell  with  a  metal 
wire,  a  difference  in  the  electrical 
condition  of  the  two  terminals 
causes  an  electric  current  to  flow 
along  the  wire.  The  fact  that  the 
wire  gets  hot  and  that  a  bell  rings 
when  the  button  is  pushed  (Fig. 
305)  suggests  that  something  is 
to  flow  along  the  wire.  flowing  along  the  wire.  This  we. 


A   SIMPLE  ELECTRIC  CELL 


309 


call  electricity.  We  describe  the  difference  of  electrical  con- 
dition in  the  terminals  of  the  dry  cell  as  a  difference  of  electrical 
potential,  which  tends  to 
make  electricity  flow. 

272.  A  simple  electric 
cell.  This  method  of  set- 
ting up  a  difference  of  elec- 
trical potential  and  of  main- 
taining an  electric  current 
by  chemical  action  was  dis- 
covered a  little  more  than 
a  hundred  years  ago  by 
an  Italian  scientist,  named 
Volta  (Fig.  306). 

Suppose  we  place  a  strip  of 
copper  and  a  strip  of  zinc  in  a 
tumbler  so  that  they  do  not 
touch  each  other  and  then 
pour  in  some  dilute  sulfuric 
acid  (Fig.  307).  We  observe 
that  the  copper  plate  is  not 
affected  by  the  acid,  while 


Fig.  306.  Alessandro  Volta  (1745-1827). 
Italian  physicist  who  invented  the  elec- 
tric battery,  the  electroscope,  the  elec- 
trophorus,  and  the  condenser. 


the  zinc  plate  is  soon  covered 
with  bubbles,  which  rise  to 
the  top,  the  zinc  plate  being  gradually  eaten  away. 


-SiUfuric 
Acid 

Fig.  307.    A  simple  elec- 
tric cell. 


Careful  experiments  with  a  sensitive  elec- 
troscope show  that  the  copper  plate  is  posi- 
tively charged  and  the  zinc  plate  is  negatively 
charged.  If  we  connect  the  plates  by  a  wire 
containing  an  electric  bell  and  push  button, 
an  electric  current  will  flow  through  this 
wire  from  one  plate  to  the  other,  as  is  in- 
dicated by  the  ringing  of  the  bell.  It  is 
assumed  that  the  current  flows  in  the  wire 
from  the  copper  (the  plate  of  higher  poten- 
tial) to  the  zinc  (the  plate  of  lower  potential). 


310 


ELECTRIC  CURRENTS 


Almost  any  two  electrical  conductors  might  be  used  for  the 
plates  instead  of  zinc  and  copper ;  but  the  two  plates  must 
not  be  of  the  same  material.  Likewise,  other  liquids  might 
be  used  in  place  of  the  sulfuric  acid,  but  it  is  necessary  that 
the  liquid  (called  the  electrolyte)  should  attack  one  of  the 
metals  chemically.  It  is  customary  to  call  the  plate  which  is 
attacked  the  less  readily  the  positive  (+)  electrode,  and  the 
other,  the  negative  (  — )  electrode. 

273.  An  electric  circuit.  A  current  of  electricity  will  not 
flow  unless  there  is  a  complete  conducting  path  or  ring.  Such 
a  path  through  which  the  current  flows  is  called  an  electric 
circuit.  That  portion  of  the  circuit  which  is  outside  the  cell, 
including  the  electric  bell,  push  button,  and  connecting  wires, 
is  called  the  external  circuit ;  that  part  which  is  inside  the  cell 
itself,  namely,  the  plates  and  the  liquid,  is  called  the  internal 
circuit.  It  will  be  noted  that  the  current  in  the  external  circuit 
flows  from  the  copper  (or  carbon)  to  the  zinc  through  the  metal 
wires,  and  that  its  path  is  completed  by  the  internal  circuit 
from  the  zinc  to  the  copper  (or  carbon)  through  the  liquid. 

If  we  cut  the  wire  outside  the  liquid, 
that  is,  break  the  circuit,  the  difference 
of  potential  will  still  remain,  but  no 
current  can  then  flow  because  the  con- 
ducting path  is  broken.  If  we  again 
join  the  ends  of  the  wire,  that  is, 
make  or  close  the  circuit,  the  current 
again  flows. 

274.   Hydraulic  analogy.     The  ac- 
tion  of  a  simple  electric  cell  like  that 
Fig.  308.  Hydraulic  analogue  of  just  described  may  be  compared  to  a 

pump  for  circulating  water  through  a 

system  of  pipes.     A  cell  may  be  considered  as  a  machine  for 
pumping  electricity. 

Suppose  two  deep  tanks,  A  and  B  in  figure  308,  are  placed  so  that 
A  stands  on  a  higher  level  than  B.  A  pipe  with  a  pump  P  leads  -from 


UNIT  OF  CURRENT.      THE  AMPERE 


311 


the  bottom  of  B  to  the  bottom  of  A.  If  the  tanks  are  partly  full  of 
water  and  the  pump  is  started,  water  will  be  drawn  from  the  tank  B 
into  the  tank  A,  thus  raising  the  water  level  in  the  latter.  If  an  over- 
flow pipe  is  carried  from  tank  A  to  tank  B,  the  overflow  will  run  back 
into  the  depleted  tank,  and  the  water  will  simply  be  circulated  by  the 
pump  in  a  current  flowing  through  the  system  of  pipes  and  the  two 
tanks.  This  is  somewhat  like 
the  electric  cell  when  the  ex- 
ternal circuit  is  closed. 

Now  if  the  overflow  pipe  is 
closed  by  a  valve  F,  the  pump 
will  soon  empty  the  tank  B ; 
after  this  it  may  continue  to 
run,  but  it  cannot  pump  any 
water,  and  no  current  of  water 
will  flow  through  the  pipes. 

This  is  similar  to  the  condi- 
tion in  an  electric  cell  which 
does  not  have  its  terminals  con- 
nected by  a  wire.  The  plates 
will  be  maintained  at  a  differ- 
ence of  electrical  potential,  but 
no  current  flows. 

275.  Unit  of  current.  The 
ampere.  The  rate  of  a 
current  of  water  flowing 
through  a  pipe  may  be  ex- 
pressed as  a  certain  number 
of  gallons  or  cubic  feet  per 
second.  In  the  same  way  the  rate  of  a  current  of  electricity 
may  be  expressed  as  a  certain  quantity  of  electricity  flowing  per 
second  past  a  certain  point.  The  unit  of  quantity  of  electricity 
is  called  a  coulomb  in  honor  of  the  French  scientist,  Coulomb. 
The  methods  by  which  such  a  quantity  of  electricity  may  be 
measured  are  explained  in  section  324.  An  electric  current 
carrying  one  coulomb  per  second  is  called  a  current  of  one  ampere. 
This  unit  was  named  after  the  French  physicist,  Ampere  (Fig. 
309).  Since  we  are  usually  interested  in  the  rate  of  flow  of 


Fig.  309.  Andre  Marie  Ampere  (1775-1836). 
French  physicist  and  mathematician  who 
studied  the  magnetic  effects  of  electric 
currents. 


312  ELECTRIC  CURRENTS 

electricity  and  not  the  quantity,  we  use  the  term  ampere  very 
often  and  only  rarely  the  term  coulomb. 

Thus,  a  new  dry  cell  whose  terminals  are  connected  by  a  short 
stout  wire  causes  about  20  amperes  to  flow  through  the  wire.  A 
40-watt  tungsten  lamp  takes  about  one  third  of  an  ampere,  while  the 
arc  lamps  used  for  street  lighting  require  from  5  to  10  amperes.  A 
telephone  receiver  operates  on  less  than  0.1  amperes,  while  the  motor 
on  a  street  car  often  takes  40  or  50  amperes,  and  the  starting  motor 
of  an  automobile  as  much  as  150  or  200  amperes. 

276.  Unit  of  resistance.    The  ohm.    We  are  familiar  with 
the  fact  that  a  stream  of  water  flowing  through  a  pipe  is  re- 
tarded by  the  friction  of  the  pipe.     If  the  pipe  is  long  and 
small  and  rough,  we  know  that  it  offers  a  large  resistance  to 
the  flow  of  water  through  it.     In  a  similar  way  electrical  re- 
sistance is  the  opposition  which  is  offered  by  electrical  conductors 
to  the  flow  of  current.    We  have  already  (section  259)  divided 
substances  into  two  classes,   conductors  and  nonconductors, 
or  insulators;   but  even  the  best  conductors  of  electricity  are 
not  perfect.     All  conductors  offer  some  resistance  to  the  flow 
of  electricity. 

The  unit  of  resistance  is  the  ohm,  which  is  named  after  the 
German  scientist,  Dr.  Ohm,  who  first  set  forth  the  law  in  regard 
to  electric  currents,  which  will  be  discussed  in  section  279. 

Thus,  1000  feet  of  No.  10  copper  wire  has  a  resistance  of  almost 
precisely  1  ohm.  About  157  feet  of  No.  18  copper  wire  (the  size 
ordinarily  used  to  connect  electric  bells)  or  26  feet  of  iron  wire  or  6 
feet  of  manganin  wire  of  the  same  size  has  a  resistance  of  1  ohm.  A 
2^-inch  vibrating  bell  will  usually  have  a  resistance  somewhere  be- 
tween 1.5  and  3  ohms,  a  telegraph  sounder  about  4  ohms,  a  telephone 
receiver  60  ohms,  and  a  40-watt  Mazda  lamp,  when  hot,  300  ohms. 

277.  Difference  of  potential.    The  volt.     In  hydraulics  we 
know  that  in  order  to  get  water  to  flow  along  a  pipe  it  is  es- 
sential to  have  some  driving  force,  due  to  a  difference  in  water 
level,  or  to  a  pump.     In  much  the  same  way,  to  get  electricity 
to  flow  along  a  wire  we  must  have  an  electromotive  force,  such 


DISTINCTION  BETWEEN   VOLTS  AND  AMPERES     313 

as  that  furnished  by  the  difference  of  potential  of  an  electric 
cell  or  by  some  other  electric  generator.  The  unit  of  electro- 
motive force  is  called  the  volt,  after  the  Italian  scientist,  Volta, 
who  discovered  the  chemical  means  for  producing  electric 
current.  A  volt  may  be  defined  as  the  electromotive  force  needed 
to  drive  a  current  of  one  ampere  through  a  resistance  of  one  ohm. 

For  example,  the  electromotive  force  of  a  simple  cell  made  of  zinc 
and  copper  plates  and  dilute  sulfuric  acid  is  about  one  volt.  A  com- 
mon dry  cell  gives  about  1.5  volts,  and  a  storage  cell  about  2  volts. 
The  current  for  lighting  a  building  is  usually  delivered  at  110  or  220 
volts,  and  street  cars  operate  on  about  500  volts. 

Electromotive  force  (abbreviated  e.m.f.)  is  sometimes 
called  voltage  or  difference  of  potential.  All  of  these  terms 
mean  the  same  thing,  namely,  the  "  push  "  that  moves  or 
tends  to  move  electricity. 

278.  Distinction  between  volts  and  amperes.  The  intensity 
of  an  electric  current  is  measured  in  amperes ;  the  electro- 
motive force  driving  the  current  is  measured  in  volts.  In  a 
given  circuit  the  greater  the  electromotive  force  is,  the  greater 
is  the  current.  Just  as  we  must  have  a  certain  "  head  "  of 
water  in  order  to  get  a  given  number  of  gallons  of  water  to  flow 
through  a  given  pipe  per  second ;  so  we  must  have  a  certain 
electromotive  force  in  order  to  make  a  given  current  of  elec- 
tricity flow  through  a  given  wire.  With  both  water  and 
electricity  we  must  have  a  motive  force  in  order  to  have  a 
current ;  but  we  may  have  the  motive  force  and  yet  have  no 
current.  Just  as  when  the  valve  is  closed  in  a  water  pipe,  if 
the  switch  is  open  in  the  electric  circuit,  we  may  have 
motive  force  (volts)  but  no  current  (amperes). 

Since  in  our  study  of  electricity  we  shall  have  very  much 
to  do  with  electric  currents,  it  is  of  the  utmost  importance  that 
we  get  a  clear  conception  of  these  three  terms : 
(a)    current  (rate  of  flow  of  electricity), 
(6)    resistance  (opposition  which  regulates  the  flow), 
(c)   voltage  (moving  force  which  causes  the  flow). 


314 


ELECTRIC  CURRENTS 


The  following  table  will  help  to  fix  the  meaning  of  the  units r 
ampere,  ohm,  and  volt. 


UNITS  OF 

WATER 

ELECTRICITY 

Quantity 

Gallon 

Coulomb 

Current 
Quantity  per  second 

Gallon  per  second 

Ampere 
Coulomb  per  second 

Resistance 

(No  unit) 

Ohm 

Motive  force 

Feet  of  head 

Volt 

279.  Ohm's  law.  We  have  just  learned  that  we  cannot 
have  a  current  flowing  in  a  circuit  unless  there  is  an  electro- 
motive force  to  make  it  flow, 
and  that  the  amount  of  the 
current  is  regulated  by  the 
resistance  of  the  circuit. 
When  water  isf  or ced  through 
a  pipe  by  a  pump,  the  stream 
which  flows  is  directly  pro- 
portional to  the  pressure 
exerted  by  the  pump  and 
inversely  proportional  to  the 
frictional  resistance  of  the 
pipe.  In  the  same  way, 
when  a  current  of  electricity 
is  forced  along  a  wire,  the 
current  is  directly  propor- 
tional to  the  electromotive 

Fig.  310.     Georg  Simon  Ohm  (1787-1854).  ,  ,, 

German  physicist  and  discoverer  of  the      torce,  Or  voltage,  OI  the  CCJ 

law  in  electricity  bearing  his  name.  or  other  generator  and  in- 

versely proportional  to  the  resistance  of  the  circuit.     This  rela- 
tion between   current,   electromotive   force,  and  resistance  is 


OHM'S  LAW  315 

called  Ohm's  law,  because  Ohm  (Fig.  310)  was  the  first  scientist 
who  formally  announced  it  (in  1827).  The  law  may  be  stated 
thus:  The  intensity  of  the  electric  current  along  a  conductor 
equals  the  electromotive  force  divided  by  the  resistance. 

electromotive  force 

Current  = : 

resistance 

In  electrical  units : 

volts 

Amperes  =  — 

ohms 

p> 

In  symbols  :       7  =  - 

R 

where  /  =  Intensity  of  current  in  amperes, 

E  =  Electromotive  force  in  volts, 
R  =  Resistance  in  ohms. 

FOR  EXAMPLE,  suppose  we  want  to  find  the  intensity  of  the  current 
sent  through  a  resistance  of  5  ohms  by  an  electromotive  force  of  110 
volts. 

/  =  E  =  119  =  22  amperes. 
R        5 

If  we  want  to  find  the  electromotive  force  required  to  main- 
tain a  certain  current  in  a  circuit  of  known  resistance,  we  have 

E  =  IR. 

FOR  EXAMPLE,  suppose  we  want  to  find  the  voltage  required  to  send 
10  amperes  through  an  arc  lamp  if  the  resistance  (hot)  is  5.5  ohms. 

E  =  IR  =  10  X  5.5  =  55  volts. 

If  we  need  to  find  the  resistance  to  be  inserted  in  a  circuit  so 
that  the  current  will  have  a  given  intensity  when  a  known 
voltage  is  applied,  we  use  our  fundamental  equation  in  this 
form: 

'-*• 

FOR  EXAMPLE,  suppose  an  electric  heater  can  safely  carry  10  amperes. 
If  the  heater  is  used  on  a  115-volt  circuit,  what  must  be  the  value  of 
its  hot  resistance  ? 

E      115         ,  K    . 
R  =  -j  =  -TTT  =  11.5  ohms. 


316  ELECTRIC  CURRENTS 

Since  Ohm's  law  is  the  foundation  of  all  scientific  know- 
ledge of  electric  currents,  the  student  will  do  well  to  commit  it 
to  memory  and  will  save  himself  much  work  if  he  learns  the 
law  in  its  three  forms. 

It  may  be  useful  to  point  out  here  that  the  relation  expressed 
in  Ohm's  law  is  a  GENERAL  PRINCIPLE  which  is  found  to  hold 
true  throughout  the  workings  of  nature ;  namely,  that  the 
result  is  proportional  to  the  ratio  of  the  applied  force  to  the  re- 
sistance. 

PROBLEMS 

1.  How  much  current  flows  through  an  arc  lamp  which  has  15 
ohms  resistance  when  75  volts  are  applied  to  it  ? 

2.  What  current  is  produced  by  12  volts    acting  through  0.25 
ohms? 

3.  How  much  electromotive  force  is  needed  to  send  2.5  amperes 
through  (a)  2  ohms?    (6)  50  ohms? 

4.  What  is  the  hot  resistance  of  a  lamp  filament  which  uses  0.4 
amperes,  at  115  volts? 

6.   An  electric  heater  of  30  ohms  resistance  can  safely  carry  4 
amperes.     How  high  can  the  voltage  run? 

6.  An  electromagnet  takes  5  amperes  from  a  115- volt  line.     How 
much  would  it  draw  from  a  230- volt  line  ? 

7.  A  certain  electric  bell  requires  0.25  amperes.     The  resistance 
of  the  coils  in  the  bell  is  12  ohms.    What  voltage  is  needed  ? 

8.  The  resistance  of  a  telephone  receiver  is  80  ohms,  and  the 
current  required  is  0.007  amperes.     What  voltage  must  be  impressed 
across  the  receiver? 

9.  If  the  voltage  on  a  trolley  system  is  550  volts,  what  current  will 
flow  through  a  car  heater  whose  resistance  is  about  100  ohms  ? 

10.  An  electric  soldering  iron  takes  1.2  amperes  when  used  on  a 
115-volt  circuit.  What  is  the  resistance  of  the  iron? 

280.  Measurement  of  current  and  voltage.  We  have 
already  seen  that  by  inserting  a  water  meter  in  a  pipe  we  can 
easily  measure  the  quantity  of  water  passing  through  in  any 
period  of  time.  Then  we  can  readily  compute  the  average 
rate  of  flow,  or  the  quantity  flowing  past  any  point  per  second. 


MEASUREMENT  OF  CURRENT  AND   VOLTAGE     317 


To  measure  the  rate  of  flow  of  an  electric  current,  we  have 
simply  to  insert  an  ammeter  (contracted  from  amperemeter). 

Figure  311  shows  an  ammeter  inserted  in  the  circuit  of  an  electric 
lamp  to  measure  the  current  flowing  through  the  lamp.  It  will  be 
seen  that  all  the  current  passing  through  the 
lamp  must  go  through  the  ammeter.  The  am- 
meter itself  has  very  little  resistance ;  it  is  built 
as  delicately  as  a  watch,  and  so  must  be  handled 
with  great  care.  It  will  also  be  noted  that  the 
ammeter  is  connected  so  that  the  current  enters 
the  instrument  at  the  plus  (+)  binding  post 
and  leaves  at  the  minus  ( — )  terminal. 

To  measure  the  electromotive  force,  or 
voltage,  which  causes  a   current  to  flow  Fig.  3".    The  ammeter 

,      .    .      ,  -,          A  measures  the  cur- 

through  any  electrical  apparatus,  we  do  rent  flowing  through 
not  break  the  circuit  or  interrupt  the  the  lamP L- 
current  flowing  through  it.  We  simply  tap  the  terminals  of  the 
voltmeter  on  to  the  terminals  of  the  apparatus.  It  will  be  seen 
that  the  current  which  flows  through  the  apparatus  does  not 
flow  through  the  voltmeter. 

Figure  312  shows  how  a  voltmeter  should  be  connected  to  measure 
the  electromotive  force  which  causes  current  to  flow  through  a  lamp. 
It  will  be  seen  at  once  that  the  voltmeter  is  con- 
—     nected  across  the  lamp,  so  that  the  plus  (+) 
binding  post  of  the  voltmeter  is  joined  to  the 
plus  (+)  side  of  the  lamp.      The  voltmeter  is 
an  instrument  of  very  high  resistance  and  so 
draws    only    a  very    small    current     through 
itself. 


It  is  very  important  to  learn  the  correct 
—    use  of  the  ammeter  and  voltmeter.     An 
F1F  m«asurherthfvdet-  ammeter  is  inserted  into  the  circuit,  while 
age  across  the  lamp  L.  the  voltmeter  is  merely  tapped  across  the 
circuit.     //  an  ammeter  were  by  mistake 
tapped  across  a   line,  it  would  instantly  be  burned  out  by  the 
big  surge  of  current. 


318 


ELECTRIC  CURRENTS 


281.   Measurement  of  resistance.    Voltmeter  and  ammeter 
method.      The    simplest    method    of     measuring     resistance, 

wherever  extreme  accuracy 
is  not  required,  makes  use 
of  the  common  instruments, 
voltmeter  and  ammeter. 
Suppose  the  unknown  re- 
sistance to  be  measured  is  R. 
It  is  connected  in  series 
with  the  ammeter,  and  the 
voltmeter  is  placed  across 
the  unknown  resistance,  as 
shown  in  figure  313.  Ap- 
plying Ohm's  law,  we  have 
the  resistance  equal  to  the  voltage  divided  by  the  current  ; 
that  is, 


Ammeter 


1 — vwvwwv — 

R 

Fig.  313.     The  voltmeter-ammeter  method 
of  measuring  the  resistance  R. 


NOTE.  When  the  resistance  to  be  measured  is  high,  and  the  current 
in  the  circuit  is  small,  the  voltmeter  is  generally  connected  around 
both  the  resistance  and  the  ammeter  ;  because  voltage  across  the  am- 
meter is  a  smaller  fraction  of  the  whole  voltage  than  the  current 
through  the  voltmeter  is  of  the  whole  current. 

282.  Computation  of  the  resistance  of  a  wire.  The  resistance 
of  a  wire  depends  upon  four  things  :  its  material,  length,  cross 
section,  and  temperature.  Experiments  show  that  the  resistance 
of  any  conductor  varies  directly  as  its  length  and  inversely  as 
its  area  of  cross  section. 

Since  wires  are  usually  round,  it  is  inconvenient  to  compute 
their  area  of  cross  section  in  square  inches.  Consequently 
electrical  engineers  call  a  wire  which  is  one  thousandth  (0.001) 
of  an  inch  in  diameter  1  mil  in  diameter,  and  its  area  of  cross 
section  1  circular  mil.  Inasmuch  as  the  areas  of  circles  vary 
as  the  squares  of  their  diameters,  the  area  of  a  wire  expressed  in 
circular  mils  is  equal  to  the  square  of  its  diameter  expressed  in  mils. 


THE  RESISTANCE  OF  A    WIRE 


319 


FOR  EXAMPLE,  a  wire  which  is  15  mils  in  diameter  is  (15)2,  or  225 
circular  mils  in  cross  section.  A  wire  which  is  1  inch  in  diameter  is 
1000  mils  in  diameter  and  1  million  circular  mils  in  area.  A  square 
inch  is  4/w  million  circular  mils  in  area  (Fig.  314). 

The  resistance  of  a  wire  is  usually  computed  by  comparing 
it  with  the  resistance  of  a  piece  of  wire  of  the  same  material 
which  is  1  foot  long  and 
1  circular  mil  in  area  of 

cross  section.     Such  a 

i    / 

Area 

1  million 

circular 

mils 


Area 
1,273,000 

circular 
mils 


Fig.  314.     A  circle  and  a  square  in  circular  mils. 


piece  of  wire  is  called  a 
mil  foot  of  wire. 

The  resistance  of  a 
mil  foot  of  wire  is  some- 
times called  the  resistiv- 
ity or  specific  resistance 
of  the  substance  of 
which  the  wire  is  made. 
For  example,  the  specific  resistance  in  ohms  per  mil  foot  of 
copper  at  20°  C.  is  about  10.4,  of  aluminum  18.7,  and  of 
iron  64. 

We  can  readily  compute  the  resistance  of  any  wire  by  mul- 
tiplying the  resistance  of  a  mil  foot  of  the  wire  (given  in  ohms) 
by  the  total  length  in  feet,  and  dividing  by  its  cross  section  in  cir- 
cular mils. 

This  may  be  expressed,  for  convenience,  as  follows  : 

Kl 

= 


where  R  is  the  resistance  in  ohms,  K  the  resistance  of  a  mil  foot 
(which  is  10.4  ohms  for  copper  at  20°  C.),  I  the  length  in  feet, 
and  d2  the  circular  mils  in  cross  section. 

FOR  EXAMPLE,  in  computing  the  resistance  of  500  feet  of  copper 
wire  which  is  40.3  mils  in  diameter,  we  have 


R  =  Kl=  10.4X500 


(43.2)2 


3.2  ohms. 


320  ELECTRIC  CURRENTS 

PROBLEMS 

1.  Find  the  area  of  cross  section  in  circular  mils  of  a  round  wire  -J- 
of  an  inch  in  diameter. 

2.  What  is  the  diameter  (mils)  of  a  wire  whose  cross-sectional  area 
is  22,500  circular  mils? 

3.  What  is  the  resistance  of  a  mile  of  copper  wire  0.25  inches  in 
diameter  ? 

4.  How  long  must  a  copper  wire  0.064  inches  in  diameter  be  to  have 
a  resistance  of  10  ohms  ? 

5.  What  is  the  diameter  of  a  copper  wire   if  a  piece  1000  feet  long 
has  a  resistance  of  one  ohm  ? 

6.  What  is  the  resistance  of  a  mile  of  aluminum  wire  0.204  inches 
in  diameter? 

7.  A  copper  rod  1  inch  in  diameter  and  10  feet  long  is  drawn  out 
into  wire  0.1  inches  in  diameter.     What  is  the  resistance  (a)  of  the 
rod ;    (6)  of  the  wire  ? 

8.  Copper  weighs  0.32  pounds  per  cubic  inch.     A  coil  containing 
1000  feet  of  wire  weighs  38.4  pounds,     (a)  What  is  the  area  of  the 
wire  in  circular  mils  ?     (6)  What  is  the  resistance  of  the  coil  ? 

283.  Use  of  a  copper-wire  table.  Copper  wire  is  ordi- 
narily manufactured  only  in  certain  standard  sizes.  In  this 
country  these  sizes  are  arranged  according  to  the  Brown  and 
Sharpe  (B.  &  S.)  Gauge,  sometimes  called  the  American  Wire 
Gauge  (A.W.G.).  The  table  on  page  321  gives  a  list  of  the 
standard  sizes,  of  which  only  the  even  numbers  are  in  general 
use,  except  in  the  very  small  sizes.  The  second  column  shows 
the  diameter  of  each  gauge  number  in  mils  (0.001 ").  The 
third  column  gives  the  area  of  cross  section  in  circular  mils, 
which  we  have  already  learned  is  the  square  of  the  diameter 
in  mils.  The  fourth  column  gives  the  resistance  per  thousand 
feet  at  20°  C.  The  use  of  this  table  greatly  simplifies  all  wire 
computations.  It  will  be  seen  that  the  wires  grow  smaller  as 
the  numbers  increase  and  that  every  third  gauge  number  halves 
the  area  of  cross  section  and  doubles  the  resistance. 


COPPER-WIRE   TABLE 


321 


RESISTANCE  OF  SOFT  OR  ANNEALED  COPPER  WIRE 


B.  &S. 
GAUGE 
No. 

DIAMETER 
IN  MILS, 
d 

AREA  IN 
CIRCUI.AR 
MILS, 

d2 

OHMS  PER 
1000  FT. 

AT  20°  C. 

OR  68°  F. 

B.&S. 
GAUGE 
No. 

DIAMETER 
IN  MILS, 
d 

AREA  IN 
CIRCULAR 
MILS, 
& 

OHMS  PER 
1000  FT. 

AT    20°    C. 

OR  68°  F. 

1 

289.30 

83,694 

0.1237 

21 

28.462 

810.10 

12.78 

2 

257.63 

66,373 

0.1560 

22 

25.347 

642.40 

16.12 

3 

229.42 

52,634 

0.1967 

23 

22.571 

509.45 

20.32 

4 

204.31 

41,742 

0.2480 

24 

20.100 

404.01 

25.63 

5 

181.94 

33,102 

0.3128 

25 

17.900 

320.40 

32.31 

6 

162.02 

26,250 

0.3944 

26 

15.940 

254.10 

40.75 

7 

144.28 

20,816 

0.4973 

27 

14.195 

201.50 

51.38 

8 

129.49 

16,509 

0.6271 

28 

12.641 

159.79 

64.79 

9 

114.43 

13,094 

0.7908 

29 

11.257 

126.72 

81.70 

10 

101.89 

10,381 

0.9972 

30 

10.025 

100.50 

103.0 

11 

90.742 

8,234.0 

1.257 

31 

8.928 

79.70 

129.9 

12 

80.808 

6,529.9 

1.586 

32 

7.950 

63.21 

163.8 

13 

71.961 

5,178.4 

1.999 

33 

7.080 

50.13 

206.6 

14 

64.084 

4,106.8 

2.521 

34 

6.305 

39.75 

260.5 

15 

57.068 

3,256.7 

3.179 

35 

5.615 

31.52 

328.4 

16 

50.820 

2,582.9 

4.009 

36 

5.000 

25.00 

414.2 

17 

45.257 

2,048.2 

5.055 

37 

4.453 

19.82 

522.2 

18 

40.303 

1,624.3 

6.374 

38 

3.965 

15.72 

658.6 

19 

35.890 

1,288.1 

8.038 

39 

3.531 

12.47 

830.4 

20 

31.961 

1,021.5 

10.14 

40 

3.145 

9.89 

1,047. 

PROBLEMS 

1.  What  is  the  resistance  per  mile  of  No.  10  copper  wire? 

2.  What  size  of  copper  wire  has  about  2.5  ohms  per  mile  ? 

3.  A  coil  of  No.  20  wire  is  found  to  have  a  resistance  of  40  ohms. 
How  many  feet  are  there  in  the  coil? 

4.  An  electromagnet  contains  a  coil  of  800  turns  of  No.  24  copper 
wire.     If  the  average  length  of  a  turn  is  10  inches,  what  is  the  re- 
sistance of  the  coil  ? 

6.   What  is  the  resistance  of  1000  feet  of  cable  made  up  of  91  wires, 
each  No.  14  in  size? 


322 


ELECTRIC  CURRENTS 


284.  Effect  of  temperature  on  resistance.     If  we  coil  about 
10  feet  of  No.  30  iron  wire  around  a  piece  of  asbestos  board  and  send 
a  current  through  it,  we  find  by  m^ans  of  an  ammeter  in  series  with 

the  coil  (Fig.  315)  that  as  we  heat 
the  wire  in  a-  Bunsen  flame,  the 
intensity  of  the  current  becomes 
greatly  reduced. 

Experiments  show  that  while 
the  resistance  of  1  mil  foot  of 
copper  wire  at  20°  C.  (68°  F.) 
is  10.4  ohms,  yet  at  0°  C.  it  is 
9.6  ohms.  The  resistance  of  a 

Fig.   315-     Heating   the    iron   wire    in-    one-ohm  coil  of  Copper,  Correct 
creases  its  resistance  and  decreases  the      4.  r\o  r<     •  ±u 

current,  as  shown  by  the  ammeter.  at  °  C->  increases  as  the  tem- 
perature rises,  approximately 

0.00426  ohms  for  each  degree.  By  carefully  measuring  the 
resistance  of  a  wire  when  cold  and  then  when  hot,  we  have  an 
electrical  method  of  measuring  temperature. 

Most  pure  metals  have  nearly  the  same  rate  of  increase  of 
resistance  with  rise  of  temperature.  Thus,  the  resistance  of  a 
tungsten  (Mazda)  lamp  when  cold  is  20  ohms,  but  the  resis- 
tance of  the  same  lamp  when  the  filament  is  white  hot  rises 
to  400  ohms.  Most  alloys  of  metals  not  only  have  a  much 
higher  resistance  than  the  pure  metals  of  which  they  are  made, 
but  are  much  less  affected  by  temperature  changes.  For 
example,  "  manganin  "  is  an  alloy  of  copper,  nickel,  iron,  and 
manganese,  which  has  a  specific  resistance  of  from  250  to  450 
ohms  per  mil  foot,  according  to  the  proportion  of  the  metals 
used;  but  its  resistance  shows  scarcely  any  -change  with 
temperature. 

There  are  a  few  substances,  such  as  carbon,  glass,  and  por- 
celain, which  decrease  in  resistance  when  heated.  For  example, 
the  resistance  of  a  carbon-filament  lamp  when  it  is  hot  is  about 
half  of  the  resistance  of  the  same  filament  when  it  is  cold. 

285.  Series    circuits.     When    several    pieces    of    electrical 
apparatus  are  connected  in  tandem,  or  one  after  the  other, 


PARTIAL    CIRCUITS 


323 


they  are  said  to  be  in  series.  The  current  passes  around  its 
circuit  in  a  single  path  and  is  the  same  in  all  parts  of  the  circuit, 
no  matter  what  the  resistance  may  be.  The  path  may  be 
made  up  of  different  materials  which  are  of  various  dimensions, 
but  the  resistance  of  the  whole  is  the  sum  of  the  resistance  of  all 
the  parts. 

FOR  EXAMPLE,  suppose  we  have  three  pieces  of  apparatus  joined 
in  series,  A  50  ohms,  B  30  ohms,  and  C  16  ohms  (Fig.  316).     Then 


-ISO  volts 


1.25  amperes ' 


? 

s  A, 

C 
A   A 

1.25  amperes 

V  M 

hms 

16 

ohms 

|      50  ohms 


Fig.  316.     Three  resistances  A,  B,  and  C,  joined  in  series. 

the  total  resistance  is  the  sum  of  these  resistances,  or  50  +  30  +  16  = 
96  ohms.  If  these  are  connected  to  a  120-volt  line,  then  the  current 
according  to  Ohm's  law  is 

E       120 

~R  =  ~96~  =  amperes. 

286.   Application  of  Ohm's  law   to   partial   circuits.     It  is 

very  important  to  remember  that  Ohm's  law  applies  not  only 
to  an  entire  circuit  but  also  to  any  part  of  a  circuit.  That  is, 
the  current  in  a  certain  part  of  a  circuit  equals  the  voltage  across 
that  same  part  divided  by  the  resistance  of  the  part. 

FOR  EXAMPLE,  we  wish  to  find  the  voltage  across  the  50-ohm 
resistance  in  the  preceding  problem.  Since  the  current  is  1.25 
amperes,  we  have 

E  =  IR  =  1.25  X  50  =  62.5  volts. 
The  voltage  across  the  30-ohm  resistance  is 

E  =  IR  =  1.25  X  30  =  37.5  volts. 
Finally,  the  voltage  across  the  16-ohm  resistance  is 

E  =  IR  =  1.25  X  16  =  20  volts. 

The  total  voltage  is  the  sum  of  these  separate  voltages,  or 
62.5  +  37.5  +  20  =  120  volts. 


324  ELECTRIC  CURRENTS 

The  laws  governing  series  circuits  are  as  follows : 

The  current  in  every  part  of  a  series  circuit  is  the  same. 

The  resistance  of  several  resistances  in  series  is  the  sum  of  the 
separate  resistances. 

The  voltage  across  several  resistances  in  series  is  equal  to  the 
sum  of  the  voltages  across  the  separate  resistances. 

Moreover,  since  the  voltage  is  equal  to  the  resistance  times 
the  current  (E  =  IK),  and  since  the  current  (7)  in  every  part 
of  a  series  circuit  is  the  same,  it  follows  that  the  voltage  across 
any  part  of  a  series  circuit  is  proportional  to  the  resistance  of  that 
part. 

287.  Parallel  circuits.  When  two  or  more  pieces  of  electrical 
apparatus  are  connected  side  by  side  so  that  the  current  is 
divided  between  them,  they  are  said  to  be  in  parallel  or  in 
multiple. 

Figure  317  shows  two  wires,  whose  resistances  are  4  ohms  and  6  ohms 
respectively,  joined  in  parallel,  and  the  voltage  between  their  ter- 
4ohm3  minals  (the  points  A  and  B) 

<•»>-*  x"  '^B,^™    js  I2  ™lts.     Applying  Ohm's 

law,  we  find  the  current  flow- 
ing along  the  4-ohm  wire  is 
^r  =  3  amperes,  and  that 
through  the  6-ohm  wire  is 

^F-  =  2  amperes.     It   will  be 
Two  wires  joined  in  parallel.  , 

seen  that  the  larger  current, 

3  amperes,  flows  through  the  smaller  resistance,  4  ohms.  Also,  the 
total  current  flowing  through  the  circuit  containing  the  two  wires  in 
parallel  is  2  +  3,  or  5  amperes.  We  may  find  the  joint  resistance 
of  the  two  wires  in  parallel,  or  the  resistance  of  the  circuit  between 
A  and  B,  by  applying  Ohm's  law.  The  voltage  between  A  and  B  is 
12  volts  and  the  current  is  5  amperes ;  therefore  the  resistance  must  be 

R  =  j-  =  -=-  =  2.4  ohms. 
1        o 

Thus  we  see  that  the  joint  resistance  of  two  wires  in  parallel 
is  less  than  the  resistance  of  either  wire  alone.  But  this  is  ex- 
plained by  considering  that  the  more  paths  we  have  in  parallel 


PARALLEL  CIRCUITS 


325 


between  A  and  B  to  carry  the  current,  the  less  the  resistance 
between  those  points.  If  we  had  three  wires  in  parallel,  the 
joint  resistance  would  be  still  less. 

This  is  quite  like  the  case  of  two  tanks  at  different  levels  and 
connected  by  three  pipes.  Evidently  more  water  will  flow 
through  two  pipes  in  a  given  time  than  through  one  alone,  and 
still  more  will  flow  through  three  pipes.  Hence,  as  pipes  are 
added  between  the  tanks,  the  resistance  controlling  the  total 
flow  of  water  is  decreased. 

To  find  the  joint  resistance  of  a  parallel  circuit,  first  find  the 
current    through    each    branch.      Then    add    these    currents 
to   find   the    total    current. 
Finally,  divide   the  voltage 
across  the  parallel  circuit  by 
this  total  current.      In  case 
the    voltage    is   not    given, 
assume  it  to  be  one  volt. 


0.2  amperes 


Thfee  resistances  LM 
joined  in  parallel. 


Assume  that  the  voltage  across 


FOR  EXAMPLE,  we  have  (Fig 
318)  three  resistances  L,  M,  and 
N   in    parallel.      L  =  8  ohms, 
M  =  16  ohms,  and  N  =  80  ohms. 
the  combination  is  1  volt. 

Then  the  current  in  L  is  •§-,  or  0.125  amperes,  in  M  is  TV,  or  0.0625 
amperes,  and  in  N  is  ^j-,  or  0.0125  amperes.  The  total  current  is  0.125 
+  0.0625  +  0.0125  =  0.2  amperes,  and  the  joint  resistance  is  ^,  or  5 
ohms. 

A  little  consideration  of  what  precedes  will  show  that  when 
two  wires  of  equal  resistance  are  connected  in  parallel,  their 
joint  resistance  is  just  half  as  great  as  the  resistance  of  either 
wire.  If  three  wires  of  equal  resistance  are  connected  in  paral- 
lel, their  joint  resistance  is  just  one  third  as  great  as  the  re- 
sistance of  one  of  the  conductors,  and  so  on.  If  wires  of  equal 
resistance  were  connected  in  series  instead  of  in  parallel,  the 
resistances  would  be  two,  three,  and  so  on,  times  as  great  as 
that  of  a  single  wire. 


326  ELECTRIC   CURRENTS 

The  laws  governing  parallel  circuits  are  as  follows : 

The  voltage  across  several  resistances  in  parallel  is  the  same 
far  all. 

The  total  current  through  the  combination  is  the  sum  of  the  cur- 
rents through  the  parts. 

The  joint  resistance  of  a  parallel  combination  is  equal  to  the 
voltage  divided  by  the  total  current. 

PROBLEMS 

1.  If  a  lamp  having  45  ohms  resistance  is  joined  in  series  with  a 
coil  of  10  ohms  across  a  110- volt  circuit,  what  is  the  resistance  of  the 
two  pieces  joined  in  series  ?     What  is  the  current  ? 

2.  Three  resistances,  200,  200,  and  40  ohms,  are  connected  in  series 
across  a  220- volt  line.     What  is  the  resistance  of  this  part  of  the  cir- 
cuit ?     What  current  flows  in  this  circuit  ? 

3.  If  five  lamps  of  15  ohms  each  are  inserted  in  series  in  a  line 
whose  resistance  is  4  ohms,  what  is  the  total  resistance  ?     What  voltage 
is  needed  to  send  7  amperes  through  the  lamps  ? 

4.  A  lamp  of  55  ohms,  another  lamp  of  30  ohms,  and  a  coil  of  15 
ohms  are  connected  in  series.     The  voltage  across  the  30-ohm  lamp 
is  120  volts. 

Find: 

(a)    The  current  in  the  lamps  and  the  coil. 
(6)    The  voltage  across  the  55-ohm  lamp. 
(c)    The  total  voltage. 

6.    Three  resistances,  one  30  ohms,  another  40  ohms,  and  the  third 
unknown,  are  connected  in  series  with  an  ammeter  which  reads  2.5 
amperes.     Total  voltage  on  the  line  is  225  volts. 
Find: 

(a)    The  unknown  resistance. 
(6)    The  voltage  across  30  ohms, 
(c)    The  voltage  across  40  ohms. 

6.  What  is  the  joint  resistance  of  three  parallel  branches,  each  of 
which  has  a  resistance  of  120  ohms  ? 

7.  What  is  the  joint  resistance  of  two  parallel   branches  which 
have  resistances  of  40  and  60  ohms  respectively  ? 

8.  If  the  resistance  of  a  wire  is  4  ohms,  what  must  be  the  resistance 
of  another  which,  when  put  in  parallel  with  it,  makes  the  joint  re- 
sistance 3  ohms  ? 


CELLS  IN  SERIES 


327 


9.   What  is  the  joint  resistance  of  three  wires  in  parallel  which 
have  resistances  of  1,  0.5,  and  0.2  ohms  respectively? 

10.  If  ten  similar  lamps,  connected  in  parallel,  have  a  joint  re- 
sistance of  20  ohms,  what  is  the  resistance  of  each  lamp  ? 

11.  An  electromotive  force  of  150  volts  is  impressed  on  a  parallel 
circuit  which  consists  of  four  branches  of  2,  4,  5,  and  10  ohms  respec- 
tively,    (a)    What    current    will    flow    in    each   branch?     (6)    What 
will  be  the  total  current  through  the  combination? 

12.  What  voltage  is  needed  to  send  9  amperes  through  a  parallel 
combination  consisting  of  a  4-ohm  and  a  12-ohm  branch  ? 

13.  A  circuit  has  three  branches  of  12,  6,  and  4  ohms  respectively. 
If  the  current  in  the  6-ohm  branch  is  4  amperes,  what  current  will  flow 
in  each  of  the  others  ? 

288.  Cells  in  series.  Not  only  may  the  separate  external 
resistances  be  arranged  in  series,  but  the  cells,  or  generators, 
themselves  may  be  so  arranged.  Figure  319 
shows  three  dry  cells  connected  in  series : 
that  is,  the  carbon  (or  -f  pole)  of  cell 
No.  1  is  connected  to  the  zinc  (or  —  pole) 
of  cell  No.  2 ;  the  carbon  of  No.  2  is  con- 
nected to  the  zinc  of  cell  No.  3;  and  the 
current  for  the  external  circuit  is  led  off 
from  the  carbon  of  cell  No.  3.  After 
passing  through  the  external  circuit,  the  Fig- 319.  Three  cells  con- 

'  nected  in  series. 

current  returns  to  the  zinc  of  cell  No.  1. 
Thus  we  see  that  the  current  flows  through  each  cell  in  suc- 
cession. 

If  we  test  one  dry  cell  with  a  voltmeter,  we  find  that  it  gives 
an  electromotive  force  of  about  1.5  volts,  two  cells  in  series 
give  3.0  volts,  and  three  cells  in  series  give  4.5  volts ;  so  the 
e.m.f.  of  a  combination  of  cells  in  series  is  the  sum  of  the  e.m.f. 's 
of  the  cells. 

It  may  help  us  to  understand  why  the  e.m.f .  of  cells  in  series 
is  the  sum  of  the  several  e.m.f. 's  if  we  think  of  the  first  cell 
.as  pumping  the  electricity  up  to  a  certain  electrical  potential 


328 


ELECTRIC  CURRENTS 


(or  level),  and  the  next  cell  as  pumping 
it  to  a  still  higher  potential  and  so  on. 
Figure  320  shows  the  water  analogy  of 
3  cells  in  series. 

Of  course,  the  internal  resistance  of  a 
combination  of  cells  in  series,  like  the 
resistance  of  any  series  circuit,  is  the  sum 
of  the  internal  resistances  of  the  single 
cells. 

289.   Cells  in  parallel.     Any  combina- 

Fig.  320.  Water  analogue  of  tion    Qf    two    or    more    ce[\s    js    caHed    a 
three  cells  in  senes.  .  .     . 

battery.  Sometimes  it  is  advantageous  to 
arrange  cells,  or  generators,  in  parallel.  Figure  321  shows  a 
battery  of  three  dry  cells  arranged  in  parallel  ;  that  is,  all  the 
positive  terminals  (carbons)  are  connected 
together  and  so  are  all  the  negative  ter- 
minals (zincs).  If  we  test  the  e.m.f.  of 
this  parallel  combination,  we  find  that 
the  voltage  of  a  parallel  battery  is  the  same 
as  the  voltage  of  one  cell. 

It  will  help  us  to  understand  why  the 
e.m.f.  of  cells  in  parallel  is  no  greater 
than  that  of  a  single  cell  if  we  think  of 
each  cell  as  pumping  the  electricity  up 


>£ 

M 

$ 

to  a  certain  electrical  potential  (or  level)  Fig- 
and  all  the  cells  as  working  side  by  side. 
Figure  322  shows  the  water  analogy  of  cells  in  parallel. 
The  internal  resistance  of  a  parallel  battery,  like  that  of  any  other 
parallel  combination,  is  the  resistance  of 
one  cell  divided  by  the  number  of  cells. 

FOR  EXAMPLE,  suppose  that  3  cells  are  in 
parallel,  that  the  voltage  of  each  cell  is  1.5 

-^_  volts,  and  that  the  resistance  of  each  cell  is 

Fig.  322.    Water  analogue  of   °-  12  ohms.    What  will  be  the  current  through 
three  cells  in  parallel.         an  external  resistance  of  0.26  ohms  ? 


BEST  ARRANGEMENT  OF  CELLS  329 

The  internal  resistance  of  the  battery  is  -^-  ,  or  0.04  ohms.  The 
total  resistance  is  the  sum  of  the  internal  and  external  resistances, 
0.26  +  0.04  =  0.3  ohms.  By  Ohm's  law  the  current  through  the 
external  resistance  is  ^|,  or  5  amperes. 

Then  the  current  in  each  cell  will  be  ^  of  5  amperes,  or  1.67  amperes. 

290.  Best  arrangement  of  cells.  Given  6  dry  cells,  it  would 
be  possible  to  arrange  these  cells  in  two  other  ways  besides 
all  in  series  or  all  in  parallel.  For  example, 
we  might  arrange  them  in  two  rows  of  three 
cells  each,  join  the  cells  in  each  row  in  series, 
and  then  connect  the  rows  in  parallel,  as  shown 
in  figure  323.  It  would  also  be  possible  to 
arrange  the  six  cells  in  3  rows,  each  consisting  Fig  J23  Six  cells 
of  2  cells  in  series,  the  rows  being  connected  connected  3  in 


in  parallel  (Fig.  324).  ""   *  ' 


To  find  the  current  which  any   combination   of  cells  will   force 
through  a  given  resistance :  first,  find  the  total  voltage,  that  is,  the 
volts  per  cell  times  the  number  of   cells  in 
series;    second,  find   the   internal  resistance, 
which  is  the  resistance  of  one  cell  times  the 
number  of  cells  in  series  divided  by  the  num- 
ber  of   parallel  rows ;    third,    find   the   total 
resistance,  that  is,  the  sum  of  external  and 
Fig    324      Six  cells  con-  internal  resistances  ;  finally,  apply  flflfc's  law, 
nected  2  in  series  and  3  that  is,  divide  the  total  voltage  \j^f'  total 
in  parallel.  resistance. 

It  can  be  proved  that  the  maximum  current  is  obtained  by 
arranging  the  cells  so  that  the  internal  resistance  of  the  whole 
combination  of  cells  is  as  nearly  as  possible  equal  to  the  external 
resistance. 

Therefore,  to  get  the  greatest  current  through  a  given  resis- 
tance, if  the  external  resistance  is  large,  arrange  the  cells  in 
series;  but  if  the  external  resistance  is  very  small,  arrange 
the  cells  in  parallel. 

In  practical  work  the  external  resistance  is  usually  large  com- 
pared with  the  internal  resistance ;  hence  cells  are  generally 
arranged  in  series. 


, 


330 


P 


ELECTRIC   CURRENTS 


PROBLEMS 

1.  Find  the  current  which  each  of  the  four  arrangements  of  the  6 
cells  described  in  the  preceding  section  would  send  through  an  external 
resistance  of  10  ohms.     Assume  that  the  voltage  of  each  cell  is  1.5 
volts  and  that  the  internal  resistance  of  each  cell  is  0.12  ohms. 

2.  Find  the  current  which  each  of  these  four  arrangements  of  6  cells 
would  send  through  an  external  resistance  of  0.1  ohms. 

291.   Internal  construction  of  a  dry  cell.     During  the  last 
few  years,  what  is  called  a  "  dry  "  cell  has  come  to  be  practically 
the  only  type  of  cell  used  for  open-circuit  or  intermittent  work, 
such  as  ringing  bells,  and  operating  telephones,  signal  devices, 
flash  lights,  and  the  ignition  circuits  of  gas 
engines.     In  this  cell  (Fig.  325)  the  nega- 
tive plate  is  a  zinc  can,  which  serves  as 
the  containing  vessel,  and  the  positive 
plate  is  a  carbon  rod,  which  may  be  either 
cylindrical  or  fluted.      The  zinc  can  is 
lined  with  an  absorbent  layer  of   pulp 
board  or  blotting  paper  which  is  saturated 
with  a  water  solution  of  sal  ammoniac  and 
zinc  chloride.      The  space  between  the 

r  lining  and  the   carbon  is   filled  with  a 

paste  made  of  granulated  carbon  and  manganese  dioxide  soaked 
in  a  water  solution  of  sal  ammoniac.  This  mixture  fills  the 
cell  to  within  about  an  inch  of  the  top.  The  top  of  the  cell  is 
generally  sealed  up  with  a  pitch  composition.  The  outside  of 
the  zinc  can  is  frequently  lacquered  and  the  cell  is  always  set  in 
a  close-fitting  cardboard  container.  The  sal  ammoniac  in  this 
cell  takes  the  place  of  the  sulfuric  acid  in  the  simple  cell 
described  above. 

About  eighty  per  cent  of  the  dry  cells  manufactured  in  this  country 
(about  fifty  million  each  year)  are  made  with  a  zinc  can  6  inches  high  and 
2.5  inches  in  diameter.  Such  a  cell  when  new  should  give,  when  tested 
with  an  ammeter  (Fig.  326),  at  least  15  amperes  and  not  more  than 
25  amperes.  Much  smaller  dry  cells  are  made  for  flash  lights.  Tests 


Cardboard 
Zinc 
Blotting  Paper 

Paste 


Fig.    325.     Cross   sec- 
tion of  a  dry  cell. 


POLARIZATION  IN   DRY   CELLS 


331 


with  a  voltmeter  will  show  that  the  size  of  a  cell  makes  no  difference  in 
its  voltage. 

292.  How  long  will  a  dry  cell  last?  The  "  life  "  of  a  dry 
cell  is  not  a  fixed  quantity  but  depends  on  the  circuit  in  which 
it  is  used.  Oftentimes  dry  cells  which  are 
merely  standing  on  a  shelf  for  a  year  without 
being  used  at  all  will  dry  up  and  become  prac- 
tically useless.  Sometimes  a  battery  of  5  dry 
cells,  such  as  would  be  used  for  the  ignition 
of  a  gas  engine  which  is  in  pretty  constant 
use,  will  last  for  two  months.  The  working 
life  of  a  dry  cell  depends  on  the  length  of  time 
that  its  circuit  is  left  closed,  but  may  be 
extended  by  arranging  the  circuit  so  that  the 
current  drawn  from  any  one  cell  will  be  small. 

In  an  old  dry  cell  holes  will  often  be  found  in 
the  zinc  can.  This  means  that  the  metal  has  been 
consumed  by  the  chemical  change  which  furnished 
the  energy  to  drive  the  electricity  through  the  cell 
and  the  external  circuit.  Thus  we  see  that  the  zinc 


Dry  Cell 


Fig.  326.     Testing 
a  dry  cell. 


acts  as  the  fuel,  very  much  as  coal  is  iised  to  furnish  the  energy  to 
drive  water  through  pipes.  The  rate  at  which  this  electrical  energy 
is  delivered  by  the  cell  determines  the  rate  at  which  the  zinc  is  used 
up ;  just  as  the  rate  at  which  steam  energy  is  delivered  to  a  boiler 
determines  the  rate  of  coal  consumption.  A  large  cell  will  naturally 
last  longer  than  a  small  cell  because  it  contains  more  zinc.  It  is  on 
account  of  the  expense  of  using  zinc  as  a  fuel  that  we  employ  cells 
only  as  a  source  of  very  small  electric  currents,  and  use  electric 
generators  (Chapter  XVII)  for  supplying  power  for  domestic  and 
commercial  purposes. 

293.  Polarization  in  dry  cells.  It  was  long  ago  discovered 
that  when  a  simple  electric  cell  is  used  by  connecting  the  ter- 
minals with  a  wire,  the  current  does  not  remain  constant  but 
rapidly  becomes  weaker.  This  effect,  called  polarization,  was 
found  to  be  caused  by  the  formation  of  a  gas,  usually  hydrogen, 
on  the  positive  plate.  This  layer  of  gas  increases  the  internal 
resistance  of  the  cell  and  also  sets  up  an  opposing  electromotive 


332  ELECTRIC  CURRENTS 

force.  In  the  dry  cell  the  manganese  dioxide  is  put  in  to 
act  as  a  depolarizer.  Nevertheless,  because  of  this  polarization, 
a  dry  cell  cannot  be  left  on  a  closed  circuit  for  any  length  of  time. 

294.  Terminal  voltage  of  a  cell.      If  we  connect  a  voltmeter  to 
a  dry  cell,  we  find  that  its  e.m.f.  is  about  1.5  volts.     If  we  connect 
a  coil  of  high  resistance  (1000  ohms)   across   the   terminals,   the   ter- 
minal voltage,   as   indicated  by    the    voltmeter,  is  very  nearly  the 
same  as  before.     But  if  we  connect  a  short,  thick  wire  across  the 
terminals  (short-circuit  the  cell)  so  as  to  draw  a  large  current,  we  see 
by  the  voltmeter  that  the  terminal  voltage  is  much  less  than  before. 

From  this  experiment  it  is  evident  that  the  terminal  voltage 
of  a  cell  which  is  delivering  current  is  always  less  than  its 
electromotive  force,  or  its  open-circuit  voltage.  We  may 
understand  this  fact  if  we  remember  that  voltage  is  used  to  send 
the  current  through  the  internal  resistance  of  the  cell;  just 
as  voltage  is  used  to  send  a  current  through  any  other  kind 
of  resistance. 

FOR  EXAMPLE,  if  the  e.m.f.  of  a  dry  cell  is  1.5  volts  and  its  internal 
resistance  is  0.07  ohms,  what  is  the  terminal  voltage  when  it  is  de- 
livering 5  amperes  ? 

Volts  used  in  overcoming  int.  rest.  =  current  X  internal  resistance 

=  5  X  0.07 
=  0.35  volts. 

Terminal  voltage  =  e.m.f.  —  volts  used  on  internal  resistance 
=  1.5  -  0.35 
=  1.15  volts. 

If  the  current  is  10  amperes,  the  terminal  voltage  is  1.5—  10  X  0.07, 
or  0.8  volts. 

Since  some  of  the  electromotive  force  of  a  cell  must  always 
be  used  in  sending  current  through  its  internal  resistance,  it 
is  essential  that  this  internal  resistance  be  as  low  as  possible, 
especially  when  the  cell  is  to  furnish  a  large  current. 

295.  Voltage  drop  in  a  line.     We  have  just  seen  that  the 
terminal  voltage  of  a  battery  is  less  than  its  electromotive 
force    because  of  the  voltage    required  to  send  the  current 


VOLTAGE   DROP  IN  A   LINE  333 

through  the  internal  resistance  of  the  battery.  Similarly 
when  an  electric  current  is  used  at  a  considerable  distance 
from  the  generator,  the  voltage  at  the  receiving  end  of  the 
line  is  always  less  than  the  generator  voltage.  This  voltage 
drop  in  the  line  is  equal  to  the  current  times  the  resistance  of 


15  amp. 


f!5  amp. 


6  v  drop  in 
Feeder 


6  v  drop  in 
Feeder 


Fig.  327.     Voltage  drop  in  a  line  is  the  voltage  required  to  send   the   current 

through  the  line. 

the  line  (IK).  The  voltage  drop  in  ordinary  practice  for 
house  wiring  should  not  exceed  2  per  cent. 

If  we  know  the  length  and  the  size  of  a  line  wire  and  the 
current  it  is  to  carry,  we  can  compute  the  voltage  drop. 

FOR  EXAMPLE,  what  is  the  voltage  drop  in  1500  feet  of  No.  4  copper 
wire  carrying  40  amperes  ? 

According  to  the  wire  table  (page  321),  1000  feet  of  No.  4  wire  has 
a  resistance  of  0.248  ohms,  and  the  resistance  of  1500  feet  would  be 
1.5  X  0.248,  or  0.372  ohms.  The  voltage  drop  E  =  IR  =  40X0.372 
=  14.9  volts. 

Again,  suppose  the  voltage  drop  allowable  in  sending  15  amperes 
through  5000  feet  of  wire  is  12  volts  (Fig.  327).  What  size  wire  is 
required  ? 

Compute  'the  resistance  by  Ohm's  law  : 

R  =  i-  =  1|  =  0.8  ohms. 
1       lo 

Then  the  resistance  of  1000  feet  of  this  wire  is  Aj8,  or  0.16  ohms. 
According  to  the  table,  this  resistance  requires  a  wire  between  No.  2 
and  No.  3,  and  therefore  we  should  use  the  larger  size,  that  is,  No.  2. 


334  ELECTRIC   CURRENTS 

PROBLEMS 

1.  A  dry  cell  when  tested  with  a  voltmeter  showed  1.5  volts,  and 
when  tested  with  an  ammeter  whose  resistance  was  negligible,  gave 
7.5  amperes.     Find  the  internal  resistance  of  the  cell. 

2.  If  the  voltage  drop  in  a  trolley  line  carrying  150  amperes  is 
12.5  volts,  what  is  the  resistance  of  the  line  ? 

3.  What  is  the  "  line  drop,"  that  is,  voltage  drop,  in  a  4-mile  copper 
wire  carrying  100  amperes,  if  the  wire  is  0.325  inches  in  diameter  ? 

4.  If  a  group  of  lamps  which  takes  12  amperes  is  500  feet  from  the 
generator,  and  if  the  line  drop  must  not  exceed  2.6  volts,  what  size 
of  copper  wire  must  be  used  ? 

PRACTICAL  EXERCISES 

1.  Making  and  using  a  sal-ammoniac  cell.      For  full  directions  see 
Good's  Laboratory  Projects  in  Physics  (Macmillan). 

2.  Setting  up  a  miniature  light  and  power  system.     Follow  the  di- 
rections in  Good's  Laboratory  Projects. 

SUMMARY  OF  PRINCIPLES   IN   CHAPTER  XV 

Electric    current    flows    downhill,    from  -f-  to   — ,    in    outside 

circuit. 
Current   is   pumped    uphill,    from  —  to  +,  inside  of    cell,  or 

generator. 

Unit  of  current  is  ampere.     Corresponds  to  gallons  per  second. 
Unit  of  resistance  is  ohm.     Corresponds  to  friction  in  pipe. 
Unit  of  e.m.f.  is  volt.     Corresponds  to  head  of  water. 

Ohm's  law : 

electromotive  force 

Current  =  : 

resistance 

Applies  to  whole  circuit  or  to  any  part  of  circuit. 

If  applied  to  whole  circuit,  one  must  take  account  of  internal 

resistance  of  cell,  as  well  as  of  external  resistance. 
Ammeter  —  low   resistance  —  put    in    series  —  carries    whole 

current. 

Voltmeter  —  high    resistance  —  put    across    circuit  —  diverts 
small  current. 


SUMMARY  335 

Resistance  of  wire  = 

specific  resistance  (mil  foot)  X  length  (feet) 
square  of  diameter  (mils)2 

For  resistances  in  series  — 
Current  everywhere  the  same. 

Resistance  of  combination  is  sum  of  resistances  of  parts. 
Voltage  across  combination  is  sum  of  voltages  across  parts. 

For  resistances  in  parallel  — 

Voltage  across  conductors  is  the  same  for  all. 

Total  current  through  combination  is  sum  of  currents 
through  parts. 

Joint  resistance  is  equal  to  voltage  divided  by  total  cur- 
rent. 

For  cells  in  series  — 

E.m.f.  is  sum  of  e.m.f.'s  of  the  cells. 
Resistance  is  sum  of  resistances  of  the  cells. 
Current  is  the  same  in  each  cell  as  in  external  circuit. 

For  cells  in  parallel  — 

E.m.f.  is  same  as  e.m.f.  of  one  cell. 

Resistance  of  n  cells  in  parallel  is  j^th  the  resistance  of 
any  one  alone. 

Current  in  each  cell  is  j^th  the  current  in  external  cir- 
cuit. 

Electrical  energy  of  a  cell  is  supplied  by  chemical  action  of 
a  solution  on  zinc.      Zinc  is  fuel  of  cell. 

E.m.f.  of  cell  =  total  pump  action  of  cell. 

Terminal  voltage  less  than  e.m.f.   by  amount  needed  to  keep 
current  moving  through  internal  resistance  of  cell. 

Voltage  drop  in  line  is  equal   to  current  times  resistance  of 
line  (IR). 


336  ELECTRIC  CURRENTS 

QUESTIONS 

1.  Why  is  the  study  of  electricity  in  motion  so  much  more  im- 
portant than  the  study  of  electricity  at  rest  ? 

2.  Is  it  always  true  that  a  current  of  water  is  everywhere  the  same 
in  a  water  main? 

3.  A  copper  wire  and  an  iron  wire  of  the  same  cross  section  are 
found  to  have  the  same  resistance.     Which  is  the  longer  ? 

4.  What  number  (B.  &  S.)  of  copper  wire  has  a  resistance  of 
practically  1  ohm  per  1000  feet?     What  size  copper  wire  has  a  re- 
sistance of  practically  2  ohms  per  1000  feet?     How  many  numbers  do 
you  have  to  go  up  on  the  wire  gauge  to  double  the  resistance  of  the 
wire? 

6.    Is  it  true  that  in  a  divided  circuit  an  electric  current  "  always 
takes  the  line  of  least  resistance  "?     Explain. 

6.  How  may  the  joint  resistance  of  two  parallel  wires  be  found  if 
the  individual  resistances  are  known  ? 

7.  Why  is  the  joint  resistance  of  wires  in  parallel  never  equal  to 
the  average  of  the  separate  resistances? 

8.  How  may  the  joint  resistance  of  several  known  equal  resistances 
arranged  in  parallel  be  computed  ? 

9.  What  other  types  of  primary  cells  are  sometimes  used  besides 
the  dry  cell?     What  advantages  has  the  dry  cell  over  other  types? 

10.  Explain  why  a  dry  cell  which  is  really  dry  is  useless. 

11.  What  would  happen  to  a  dry  cell  if  you  tried  to  recharge  it 
from  a  generator? 

12.  How  does  the  voltage  drop  in  a  given  line  vary  with  the  cur- 
rent? 


CHAPTER  XVI 
EFFECTS   OF  AN   ELECTRIC   CURRENT 

Magnetic  effect  —  Oersted's  discovery  —  magnetic  field 
about  a  current  —  a  solenoid  —  electromagnet  —  applica- 
tions in  lifting  magnets,  bells,  telegraph,  d'Arsonval  galva- 
nometer, ammeter,  and  voltmeter. 

Heating  effect  —  fuses  and  circuit  breakers. 

Calculation  of  electric  power  —  watts  and  kilowatts  — 
electrical  energy  —  kilowatt  hours  and  joules. 

Lighting  —  vacuum  and  gas-filled  tungsten  lamps  —  open, 
inclosed,  flaming,  metallic,  and  mercury  arc  lamps. 

Chemical  effects  —  electrolysis  —  electroplating  —  electro- 
typing  —  refining  of  metals  —  silver  coulombmeter. 

Storage  batteries  —  lead  and  Edison. 


E 

HH  Current 


N 


MAGNETIC  EFFECT  OF  ELECTRIC  CURRENT 

296.  Oersted's  discovery.  In  1819  a  Danish  physicist, 
Oersted,  made  a  discovery  which  aroused  the  greatest  interest 
because  it  was  the  first  evidence  w 

of  a  connection  between  magnetism 
and  electricity.  He  found  that  if 
a  wire  connecting  the  poles  of  a 
voltaic  cell  was  held  over  a  com-  wire  ca 
pass  needle,  the  north  pole  of  the 
needle  was  deflected  toward  the 
west  when  the  current  flowed  from 
south  to  north,  as  shown  in  figure 
328 ;  while  a  wire  placed  under  the 
compass  needle  caused  the  north 
end  of  the  needle  to  be  deflected 
toward  the  east. 

337 


Fig.  328.  Current  in  wire  above 
compass  needle  deflects  compass 
needle. 


338 


EFFECTS   OF   AN  ELECTRIC  CURRENT 


EARTH'S  MAGNETISM 


J. 


297.  Magnetic  field  around  a  current.     Inasmuch  as  the 
compass  needle  indicates  the  direction  of  magnetic  lines  of 
force,  it  is  evident  from  Oersted's  experiment  that  a  current 

must  set  up  a  mag- 
netic field  at  right 
angles  to  the  con- 
ductor. 

To  make  this  clear, 
we  send  a  strong  cur- 
rent down  a  verti- 
cal wire  which  passes 
through  a  horizontal 
piece  of  cardboard. 
To  indicate  the  mag- 
netic lines  of  force,  we 
sprinkle  iron  filings  on 
the  cardboard  and  tap 
it  gently  while  the  cur- 
rent is  on.  The  filings 
arrange  themselves  in 
concentric  rings  about 
the  wire.  By  placing 

a  small  compass  at  various  positions  on  the  board,  we  see  that  the 
direction  of  these  lines  of  force  is  as  shown  in  figure  329. 

A  convenient  rule  for  remembering  the  direction  of  the  mag- 
netic flux  around  a  straight  wire  carrying  a  current  is  the  so- 
called  thumb  rule. 

//  one  grasps  the  wire  with  the  right  hand  (Fig.  330)  so  that 

the  thumb  points  in  the  direction  of  the  current,  the  fingers  will 

\  point  in  the  direction  of  the  magnetic 

\field. 

If  we  know  the  direction  of  the 
magnetic  field  near  a  conductor, 
we  can,  by  applying  this  rule,  find 
the  direction  of  the  current. 

298.  Magnetic  field  around  a  coil.     If  a  wire  carrying  a  cur- 
rent is  bent  into  a  loop,  all  the  lines  of  force  enter  the  loop  at 


Fig.  329. 


Magnetic  lines  of  force  surround  an  elec- 
tric current. 


Current  Flux 

Fig.  330.     Thumb  rule  for   mag- 
netic field  around  a  wire. 


ELECTROMAGNET 


339 


one  face  and  come  out  at  the  other  face.  If  several  loops  are 
put  together  to  form  a  coil,  practically  all  the  lines  will  thread 
the  whole  coil  and  return  to  the  other  end  outside  the  coil. 

(1)  We  may  thread  a  loose  coil  of  copper  wire  through  a  board  or* 
sheet  of  celluloid  in  such  a  way  that  when  iron  filings  are  evenly  scat-v 
tered  over  the  smooth  surface  of 
the  board,  while  a  strong  current 
is  sent  through  the  wire,  they  will 
indicate  the  lines  of  magnetic 
force  (Fig.  33 1 ) .  By  tapping  the 
board  gently  and  using  a  small 
compass,  we  can  see  the  general 
direction  of  the  lines  of  magnetic 
flux.  It  will  be  noticed  that  there 
are  a  few  circular  lines  around 


Fig.  331- 


Magnetic  flux  around  an  open 
coil. 


each  wire,  and  that  these  lines 

go  out  between  the  loops.     They 

are  called  the  "  leakage  flux  "  of 

the  coil. 

(2)    If  we  send  a  current  through  a  close-wound  coil  of  insulated 

copper  wire,  and  bring  it  near  a  compass  needle,  we  find  that  it 
behaves  like  a  bar  magnet.  If  the  current  is 
reversed,  the  poles  of  the  coil  are  reversed. 

(3)  If  we  put  a  soft-iron  core  inside  the  coil 
when  the  current  is  on,  the  iron  exerts  a  very 
strong  pull  on  bits  of  iron ;  but  when  the  current 
is  off,  the  iron  loses  this  magnetism  almost  at 
once. 

(4)  If  we  use  a  large  horseshoe  electromagnet 
(Fig.  332),  or  a  model  of  a  magnetic  hoist,  and 
considerable  current,  we  may  show  that  a  tre- 
mendous force  can  be  exerted  by   an   electro- 
magnet. 

An  iron  core  in  a  coil  of  wire  is  so  much 
more  permeable  than  air  that  the  same 
current  in  the  same  coil  produces  several 
thousand  times  as  many  lines  of  force  in 
the  iron  core  as  it  would  in  air  alone. 

Fig.  332.  Electromagnet         299     Electromagnet.      An  iron  core,  SUr- 
ior  demonstration  pur-  ,~T • .  .  „     , 

poses.  rounded  by  a  coil  of  wire,  is   called   an 


340 


EFFECTS  OF  AN  ELECTRIC  CURRENT 


Fig.  333-  Rule  for  polarity  of  coil 
carrying  current. 


electromagnet.     It  owes  its  great  utility  not  so  much  to  the 

fact  of  its  great  strength,  as  to  the  fact  that,  if  it  is  made  of 

soft  iron,  its  magnetism  can  be  controlled  at  will.  Such  an  electro- 
magnet is  a  magnet  only  when  cur- 
rent flows  through  its  coil.  When 
the  current  is  stopped,  the  iron  core 
returns  almost  to  its  natural  state. 
This  loss  of  magnetism  is,  however, 
not  absolutely  complete  ;  a  very  little 
residual  magnetism  remains  for  a 
longer  or  shorter  time. 
An  electromagnet  is  a  part  of  nearly  every  electrical  machine, 

including  the  electric  bell,  telegraph,  telephone,  generator,  and 

motor. 

To  determine  its  polarity, 

we  shall  find  it  convenient 

to  express  the  thumb  rule  as 

used  for  a  straight  wire,  in 

another  way,  as  follows : 
THUMB  RULE  FOR  A  COIL. 

Grasp  the  coil  with  the  right 

hand  so  that  the  fingers  point 

in  the  direction  of  the  current 

in  the  coil,  and  the  thumb  will 

point  to  the  north  pole  of  the 

coil  (Fig.  333). 

The  strength  of  an  elec- 
tromagnet depends  on  the 

product  of  the  strength  of 

the    current    CflmnerP^     hv     Fig"  334'    Joseph  Henry  (1799-1878).  First 
es;,    Dy         American  to  study  the  electromagnet  and 

the  number  of  loops  of  wire         the  laws  of  electromagnetic  induction. 

(turns),  that  is,  on  the  ampere  turns  of  the  coil. 

It  is  the  practice,  in  order  to  make  use  of  both  poles  of  an 
electromagnet,  to  bend  the  iron  core  and  the  coil  into  the  shape 
of  a  horseshoe. 


ELECTRIC   BELL 


341 


Lifting  magnet  handling  a  ton  of 
pig  iron. 


APPLICATIONS    OF    THE 
ELECTROMAGNET 

300.  Lifting  magnets. 

Practical  electromagnets  were 

made  in  183 1  by  Joseph  Henry 

(Fig.  334),  a  famous  American 

schoolmaster    and    scientist, 

then  teaching  in  the  academy 

at    Albany,    N.Y.,    and    by 

Faraday  in  England.  Henry's 

magnet  was  capable  of  sup- 
porting fifty  times   its   own 

weight,  which  was  considered 

very  remarkable  at  the  time. 
Magnetic  hoists  (Fig.  335) 

are   now   built   so   powerful  Fig.  335. 

that  when  the  face  of  the  iron 

core  is  brought  in  contact  with  iron  or  steel  castings  and  the 

current  is  turned  on,  the  magnets  will  lift  from  100  to  200 
pounds  of  iron  per  square  inch  of  pole  face, 
and  yet  release  the  load  of  iron  the  moment 
the  current  is  cut  off. 


301.  Electric  bell.  An  electric-bell  circuit 
usually  includes  a  battery  of  two  or  more  cells,  a 
push  button,  and  connecting  wires,  besides  the 
bell  itself  (Fig.  336).  When  the  circuit  is  closed 
by  pushing  the  button,  the  current  flows  through 
the  electric  magnet  m  and  attracts  the  armature 
A.  As  the  armature  swings  to  the  left,  it  pulls 
the  spring  C  away  from  the  screw  contact  B 
and  breaks  the  circuit.  This  stops  the  current, 
and  the  electromagnet  releases  the  armature. 
It  then  springs  back  again  and  closes  the  circuit 
at  the  screw,  and  the  whole  process  is  repeated. 
The  swinging  of  the  armature,  which  carries  a 
hammer,  causes  a  series  of  rapid  strokes  against 


336.      Diagram 
electric  bell. 


of 


342 


EFFECTS  OF  AN  ELECTRIC  CURRENT 


the  bell.    The  construction  of  the  ordinary  push 
button  is  shown  in  figure  337. 

302.  Telegraph.  The  word  "  telegraph  " 
means  an  instrument  which  "  writes  at  a  dis- 
tance," for  the  early  forms  invented  by  Samuel 
F.  B.  Morse,  in  1844,  were  designed  to  make 
dots  and  dashes  on  a  moving  strip  of  paper. 
Nowadays  the  receiving  instrument,  called 
the  sounder,  makes  a  series  of  clicks  separated 

Fig'  push  button1™"7   by  short  or  lonS    intervals  of  time  to  rep- 
resent the   dots  and   dashes,  and  the  mes- 
sage is  taken  by  ear  rather  than  by  eye. 

The  telegraph  consists  essentially  of  a  battery,  a  key,  and 
a  sounder,  as  shown 
in  figure  338. 
Storage  cells  are 
used  in  practical 
work,  but  for  experi- 
mental purposes  any 
kind  of  battery  will  Earth  Earth, 

serve.  FiS-  33$.     Simple  telegraph  circuit. 


Sounder 


Key, 


Station  A 
Battery 


'ain  Li 


The  key  (Fig.  339)  is  a  device,  something  like  a  push  button,  for 
making  and  breaking  the  circuit.  The  sounder  (Fig.  340)  consists 
of  an  electromagnet  with  a  soft-iron  armature  which  is  fastened  to 
a  metal  bar.  This  bar  is  pivoted  so  as  to  move  up  and  down. 
When  a  current  flows  through  the  electromagnet,  the  armature  is 
pulled  down;  when  the  circuit  is  broken,  a  spring  pushes  the  bar 

up  again.  Two  set  screws  above 
and  below  the  bar  limit  its  motion 
and  make  the  clicks.  As  the 
clicks  made  by  the  bar  hitting 
these  two  set  screws  are  dif- 
ferent the  ear  recognizes  the 


Adjusting  Screw* 
Contact, 


Button 


Fig.  339- 


Leg. 
Telegraph  key. 


time  between  these  two  clicks  as 
a  dot  or  a  dash  according  as  the 
key  is  depressed  a  short  or  a  long 
time. 


TELEGRAPH 


343 


-_.  r-  Spring 


'lectromagnet 

Fig.  340.    Telegraph  sounder. 


When  the  telegraph  came  into  com- 
mercial use,  it  was  found  that  the 
resistance  of  the  connecting  wires, 
called  the  line,  was  so  great  that  the 
current  was  too  feeble  to  operate  the 
sounder,  even  when  many  cells  were 
connected  in  series.  A  relay  (Fig. 
341)  is  therefore  employed  to  open 
and  close  the  circuit  of  a  local  bat- 
tery which  operates  the  sounder.  This 
relay  contains  an  electromagnet  whose 
coil  has  many  turns  of  very  small  copper  wire.  In  front  of  this  magnet 
is  a  light  iron  lever  which  is  held  away  from  the  electromagnet  by  a  very 
delicate  spring.  The  connections  are  shown  in  figure  342.  When  the 

key  in  the  main  circuit  is  closed, 
the  weak  current  excites  the  relay 
magnet  enough  to  pull  the  armature 
against  a  set  screw,  thus  closing  the 
local  circuit  which  sends  a  strong 
current  through  the  sounder. 

In  ordinary  telegraphy  it  is  cus- 
tomary to  use  a  single  wire  of  gal- 
vanized iron  or  hard-drawn  copper, 
and  to  use  the  earth  as  a  return 
circuit.  At  each  station  along  the  line  there  is  a  local  circuit  consisting 
of  battery  and  sounder,  which  is  closed  by  a  relay.  The  relay  is  operated 
by  the  main  circuit  containing  a  key  and  the  main-line  battery  or  gen- 
erator. Each  key  is  provided  with  a  switch, 
so  that  the  main  circuit  is  kept  closed  every- 
where except  at  the  station  where  the  opera- 
tor is  sending  a  message. 

Submarine  telegraphy  began  as  early  as 
1837,  but  it  was  not  till  1866  that  a  really 
successful  Atlantic  cable  was  laid.  Its  cop- 
per core  and  the  steel  sheath  act  like  the  coat- 
ings of  an  immense  Leyden  jar.  The  effect  of 
this  is  to  make  the  sending  of  messages  very 
slow.  The  impulses  received  at  the  other 
end  are  also  very  weak.  It  was  only  when  an 
exceedingly  delicate  receiving  instrument  had 
been  devised  by  Lord  Kelvin,  that  the  first 
Atlantic  cable  could  be  used  at  all. 


Fig.  341.    Telegraph  relay. 


Earth 


Fig.  342.      Diagram    of     a 
telegraph  relay  circuit. 


344 


EFFECTS  OF  AN  ELECTRIC  CURRENT 


303.  The  d'Arsonval  galvanometer.     An  instrument  which 
measures  or  detects  small  electric  currents  is  called  a  galva- 
nometer.     Modern    galvanometers 
are  built  with   a   moving   coil   and 
fixed  magnet;   they  are  called  the 
d'Arsonval  type. 

Figure  343  shows  one  form  of  gal- 
vanometer. The  horseshoe  magnet 
is  large  and  is  firmly  fastened  to  the 
base ;  while  the  coil  is  suspended  by 
a  very  fine  wire  or  metallic  ribbon, 
which  also  serves  to  lead  the  current 
out  of  the  coil.  The  current  enters  the 
coil  by  a  spiral  wire  or  ribbon  below. 
The  coil  is  wound  with  exceedingly  fine 
wire  on  a  very  light  rectangular  frame 
and  hangs  between  the  poles,  N  and  S, 
of  the  magnet.  Usually  there  is  a  soft- 
iron  cylinder  in  the  space  inside  the 
moving  frame  to  concentrate  the  mag- 
netic lines  of  force.  If  a  current  is  flowing  through  the  coil,  it  acts  like 
a  tiny  magnet  with  poles  pointing  to  the  front  and  rear,  and  tries  to 
turn  itself  so  that  these  poles  may 
get  as  near  as  possible  to  the  poles  of 
the  fixed  magnet.  The  amount  by 
which  it  is  able  to  twist  the  suspension 
wire  measures  the  current. 

304.  The  ammeter.     The  com- 
mercial ammeter  is  a  shunted,  mov- 
ing-coil galvanometer.    The  instru- 
ment (Fig.  344)  contains  a  coil  of 
fine  insulated  copper  wire,  wound 
on  a  light  frame,  and  mounted  in 
jeweled     bearings     between     the 
poles     of     a     strong     permanent 
horseshoe  magnet.     A  fixed  soft- 


Fig.  343.  Moving -coil  galva- 
nometer and  diagram  of  es- 
sential parts. 


Fig.  344.    Ammeter. 


iron  cylinder  midway  between  the  poles  of  the  magnet  con- 
centrates the  field.     The  moving  coil  rotates  in  the  gap  between 


THE   VOLTMETER 


345 


Fig.  345-    Voltmeter. 


the  core  and  the  pole  pieces.  The  coil  is  held  in  equilibrium 
by  two  spiral  springs,  which  serve  also  to  carry  the  current 
into  and  out  of  the  coil.  Only  a  small  fraction,  perhaps  0.001 
of  the  current  to  be  measured,  goes  through  the  movable  coil, 
the  major  part  being  carried  past  the 
coil  by  a  metal  strip  called  a  shunt. 
Since  the  current  through  the  coil  is 
a  constant  fraction  of  the  whole  cur- 
rent, the  pointer  which  is  attached 
to  the  moving  coil  can  be  made  to 
indicate  directly  on  a  graduated  scale 
the  number  of  amperes  in  the  total 
current. 

It  will  be  seen  that  the  resistance 
of  an  ammeter,  which  is  practically 
the  resistance  of  the  shunt,  is  very 
small,  and  that  the  whole  current  passes  through  the  instru- 
ment. 

305.  The  voltmeter.  The  commercial  voltmeter  (Fig.  345) 
is  simply  a  galvanometer  of  very  high 
resistance.  When  electromotive  force  is 
applied  to  a  galvanometer,  the  current 
it  allows  to  pass  is  proportional  to  the 
voltage,  and  so  the  scale  can  be  gradu- 
ated to  read  the  voltage  directly. 

This  will  be  understood  by  considering 
the  water  analogy  shown  in  figure  346.  It 
is  evident  that  the  current  in  the  connecting 
pipe  A  B  is  a  good  measure  of  the  difference 
in  level  between  L  and  L',  only  when  the 
current  in  A  B  is  so  small  as  not  to  change 
appreciably  the  levels  whose  difference  is  to  be  measured. 


Fig.  346.     Water    analogue 
of  voltmeter. 


The  instrument  is  usually  a  moving-coil  galvanometer,  like 
an  ammeter.  Indeed,  the  same  instrument  is  often  used  for 
either  purpose.  A  voltmeter  does  not  have  a  shunt  between  its 


346  EFFECTS  OF  AN  ELECTRIC  CURRENT 

terminals,  like  an  ammeter,  but  it  does  have  a  large  resistance  coil 
inserted  in  series,  so  that  only  a  very  small  current  passes  through 
the  instrument,  but  all  of  it  goes  through  the  moving  coil.  In 
fact,  such  a  voltmeter  gives  correct  values  only  when  the 
current  used  is  so  small  as  not  to  affect  appreciably  the  voltage 
to  be  measured. 

To  make  voltmeters  usable  over  different  ranges,  we  have 
merely  to  connect  coils  of  different  resistance  in  series  with 
the  same  galvanometer. 

QUESTIONS 

1.  An  electromagnet  is  found  to  be  too  weak  for  the  purpose  in- 
tended.    How  may  its  strength  be  increased  ? 

2.  In  looking  at  the  N-end  of  an  electromagnet,  in  which  direction 
does  the  current  go  around  the  core,  clockwise  or  counter-clockwise  ? 

3.  If  you  find  that  the  N-pole  of  a  compass  needle  held  under  a 
north  and  south  trolley  wire  points  toward  the  east,  what  is  the  di- 
rection of  the  current  in  the  wire? 

4.  What   is   the   difference  in  the  construction  of   a  relay  and  a 
sounder  that  makes  it  possible  for  a  weak  current  to  work  one  and 
not  the  other? 

PRACTICAL  EXERCISES 

1.  Installing  an  electric  bell  at  home.    Suppose  you  were  asked  to  put 
in  an  electric  bell.     Plan  the  wiring  and  locations  of  the  bell  button 
and  battery.     Make  a  list  of  all  the  materials  needed  and  the  cost  of 
each  item.     What  do  you  estimate  would  be  the  expense  of  maintain- 
ing the  battery  ? 

2.  Trouble  hunting  in  a  bell  circuit.     Suppose  an  electric  bell  in  your 
home  fails  to  ring.     Tell  just  how  you  would  locate  and  eliminate  the 
trouble. 

ELECTRIC  HEATING 

306.  Heating  by  electricity.  We  are  familiar  with  the  fact 
that  electric  cars  are  heated  by  electricity ;  we  know  that  an 
electric-light  bulb  gets  hot ;  and  we  may  have  used  or  seen  electric 


FUSES  AND  CIRCUIT  BREAKERS 


347 


flatirons  (Fig.  347) ,  toasters,  coffee  percolators  or  radiators.  But 
perhaps  we  do  not  realize  that  every  electric  current,  however 
small,  generates  heat,  since  the  heat  is  generated  so  slowly 
in  an  electric  bell, 
telegraph,  or  tele- 
phone, that  it  is 
radiated  off  with- 
out raising  the 
temperature  of  the 

wires  appreciably.  Fig.  347.     Electric  flatiron  and  heating  coils. 

It  is  this  heating 

effect,   however,    which    limits    the    output    of    a   generator; 

for  if  too  heavy  a  current  is   drawn  from  the  machine,  the 

coils  get  so  hot  that  the  insulation  is  set  on  fire. 
307.  Fuses  and   circuit    breakers.    To    protect    electrical 

machines  from  too  much  heat  caused  by  excessive  current, 

some  sort  of  "  electrical  safety  valve  "  has  to  be  inserted  in  the 

circuit.     Fuses  are  used  for  the  small  currents  in  house  lights 

and  small  motors,  and  circuit  break- 
ers for  larger  currents  in  power  sta- 
tions. The  essential  part  of  a  fuse  is 
a  strip  of  an  alloy  (Fig.  348a)  which 
melts  at  such  a  low  .temperature 

^____ that  the  melted  metal   can  do  no 

1  harm.     The  size  of  the  fuse  is  such 

<—          >         ~        r-n     that  if  by  accident  too  heavy  a  cur- 

Iy~l  "|  ~7          rtJ/ni     h      ren^  *s  sen^  through  the  wires,  the 
itTJJil      fuse  melts   and   breaks   the  circuit. 
c^=s^j     c      O^rptf       ^  fae  moment  the  fuse  melts  there 
is  an  arc  across  the  gap  which  might 
set  things  on  fire.   So  the  fuse  is  com- 
monly inclosed  in  an  asbestos  tube,  as 
in  the  "  cartridge  fuse  "  (Fig.  3486) ;  or  in  a  porcelain  cup  which 
screws  into  a  socket  like  a  lamp,  as  in  the  "  plug  fuse  "  (Fig. 
348c).     When  the  fuse  wire  melts,  it  is  said  to  "  blow  out." 


Fig.  348.  Different  types  of 
fuses :  (a)  link ;  (b)  cartridge  ; 
(c)  plug. 


348 


EFFECTS  OF  AN  ELECTRIC  CURRENT 


A  circuit  breaker  (Fig. 
349)  is  simply  a  large 
switch  which  is  auto- 
matically opened  by  an 
electromagnet  when  the 
current  is  excessive. 

CALCULATION   OF  ELEC- 
TRIC POWER 

308.  How  electric 
power  is  measured.  To 

measure  water  power,  we  must  know  the  quantity  of  water 
flowing  per  minute  and  the  "  head  "  of  the  water.     Thus 

Water  power  =  quantity  of  water  per  minute  X  head. 
Ib.  per  min.  X  ft. 
33,000 


Fig.  349.     Circuit  breaker  with  diagram. 


H.  P.  = 


To  measure  electric  power,  we  must  multiply  the  quantity 
of  electricity  flowing  per  second  —  that  is,  the  intensity  of 
the  electric  current  —  by  the  voltage.  Thus 

Electric  power  =  intensity  of  current  X  voltage. 

The  watt  is  the  unit  of  electric  power  and  may  be  defined  as 
the  power  required  to  keep  a  current  of  one  ampere  flowing 
under  a  drop,  or  "  head  ",  of  one  volt. 

Watts  =  amperes  X  volts. 

P  =  IE 
where  P  =  power  in  watts, 

/  =  current  in  amperes, 
E  =  e.m.f .  in  volts. 

Since  the  watt  is  a  very  small  unit  of  power,  we  commonly 
use  the  kilowatt  (kw.),  which  is  1000  watts. 

amperes  X  volts 


Kilowatts  = 


1000 


FOR  EXAMPLE,  if  a  lamp  draws  0.4  amperes  from  a  110- volt  circuit, 
it  is  using  power  at  the  rate  of  0.4  times  110,  or  44  watts. 


ELECTRICAL  ENERGY  349 

Again,  suppose  a  street-car  heater  has  a  resistance  of  110  ohms.  At 
what  rate  is  it  consuming  electricity  on  a  550-volt  line?  The  current 
is  -J^-jj-,  or  5  amperes,  and  the  power  is  5  times  550,  or  2750  watts,  or 
2.75  kw. 

Whenever  a  current  flows  through  a  circuit,  power  is  re- 
quired to  keep  it  flowing  against  the  resistance  of  the  circuit. 
This  power  is  equal  to  the  voltage  measured  between  the 
terminals  of  the  circuit  multiplied  by  the  current  flowing  in 
it,  provided  all  the  power  expended  in  that  part  of  the  circuit 
is  used  in  heating  it. 

That  is,  P  =  EL 

But  according  to  Ohm's  law  E  =  IR 
consequently,  P  =  IR  X  /  or  PR. 

Inasmuch  as  mechanical  power  is  reckoned  in  horse  power 
(h.  p.),  it  will  be  convenient  to  know  the  relation  of  the  unit 
of  mechanical  power  to  the  unit  of  electrical  power.  Ex- 
periment shows  that 

1  horse  power  =  746  watts. 
1  kilowatt  (kw.)  =  1.34  horse  power  (h.  p.). 

309.  Electrical  energy.  Power  means  the  rate  of  doing 
work,  or  the  rate  of  expenditure  of  energy.  The  total  work  done, 
or  electrical  energy  expended,  is  equal  to  the  product  of  the  rate 
of  doing  work  by  the  time.  Thus  if .  a  steam  engine  is  working 
at  the  rate  of  15  horse  power  for  8  hours;  it  does  8  times  15, 
or  120  horse-power  hours  of  work.  In  a  similar  way,  if  an 
electric  generator  is  delivering  electricity  at  the  rate  of  15 
kilowatts  for  8  hours,  it  does  8  times  15,  or  120  kilowatt  hours 
of  work. 

FOR  EXAMPLE,  we  buy  electricity  by  the  kilowatt  hour.  If  the 
price  is  10  cents  per  kilowatt  hour,  and  h*  a  store  uses  100  lamps  for 
3  hours,  each  consuming  electricity  at  the  rate  of  50  watts,  it  will  cost 

100  X  3  X  50  X0.10 

looo —         =SL5a 


350  EFFECTS  OF  AN  ELECTRIC  CURRENT 

310.  The  joule.     In  the  laboratory  we   often  find  it  con- 
venient to  use  a  smaller  unit  of  energy,  the  watt  second,  or  joule. 
Energy  (joules)  =  current  (amperes)  Xe.m.f.  (volts)  X time  (sec). 

Or  W  =  lEt. 

The  relation  of  the  joule  to  other  units  of  energy  in  common  use  is 
shown  in  the  following  table : 

1  joule  =  0.102  kilogram  meters 
=  0.738  foot  pounds 
=  0.238  gram  calories. 
1  B.t.u.  =  1054  joules. 

311.  How  much  heat  is  generated  by  an  electric  current? 

The  energy  delivered  to  an  electric  heating  coil,  such  as  a  flat- 
iron  or  soldering  iron,  is,  as  we  have  just  seen,  El  joules  per 
second,  or  Eli  joules  in  t  seconds.  But  since  Ohm's  law  tells 
us  that  E  =  IR,  if  there  is  no  cell,  generator,  or  motor  in  the 
part  of  the  circuit  considered,  we  have  the  alternative  state- 
ment, which  is  often  convenient  in  discussing  electric  heaters  : 

Energy  turned  into  heat  =  I2Rt  (joules), 

or,  since  a  joule  is  about  0.24  calories, 
H  =  0.24 1*  Rt 

where  H  =  heat  in  calories, 

/  =  current  in  amperes, 
R  =  resistance  in  ohms, 
t  —  time  in  seconds. 

PROBLEMS 

1.  How  much  electrical  power  (watts)  is  required  to  light  a  room 
with  5  lamps,  if  each  lamp  draws  0.4  amperes  from  a  110-volt  line? 

2.  A  street-railway  generator  is  delivering  current  to  a  trolley  line 
at  the  rate  of  1500  amperes  and  at  550  volts.     At  what  rate  (kilowatts) 
is  it  furnishing  power  ? 

3.  A  10-kilowatt  generator  is  working  at  full  load.     If  the  volt- 
meter reads  115  volts,  how  much  does  the  ammeter  read? 


TUNGSTEN  OR   MAZDA   LAMPS  351 

4.  How  many  lamps,  each  of  120  ohms  and  requiring  1.1  amperes, 
can  be  lighted  by  a  25- kw.  generator? 

6.  How  much  power  is  required  by  a  laundry  using  5  electric  flat- 
irons  of  50  ohms  each,  connected  in  parallel  on  a  110- volt  line? 

6.  How  much  will  it  cost  at  10  cents  per  kilowatt  hour  to  run  a  220- 
volt  motor  for  10  hours,  if  the  motor  draws  25  amperes  ? 

7.  Would  it  be  cheaper  to  buy  the  power  needed  in  problem  6  at  8 
cents  per  horse-power  hour? 

8.  How  much  energy  is  consumed  in  a  line  whose  resistance  is 
0.5  ohms,  and  which  carries  a  current  of  150  amperes  for  10  hours  ? 

9.  How  many  joules  of  energy  are  consumed  when  a  40-watt  lamp 
burns  10  minutes  ? 

10.  How  many  calories  of  heat  are  generated  per  hour  in  a  30-ohm 
electric  flatiron  using  4  amperes  ? 

11.  What  is  the  cost  of  each  calorie  in  problem  10,  if  the  electricity 
costs  10  cents  per  kilowatt  hour? 

12.  How  much  energy  is  turned  into  heat  each  hour  by  a  current  of 
35  amperes  in  a  wire  of  resistance  2  ohms  ? 

13.  If  88%  of  the  energy  received  by  an"  electric  lamp  is  converted 
into  heat,   how  many  calories   are   developed  in  one  hour  by  a  35- 
candle-power  lamp  drawing  0.9  amperes  at  115  volts? 

14.  "A  10-ohm  coil  of  wire  is  used  to Jieat  1000  grams  of  water  from 
15°  C.  to  75°  C.  in  10  minutes.     How  much  current  must  be  used? 

PRACTICAL  EXERCISE 

Cost  of  operating  various  electric  devices  per  hour.  Bring  to  the 
school  laboratory  all  the  electric  devices  which  you  have  at  home, 
measure  the  power  used  by  each,  and  then  compare  the  costs. 

ELECTRIC  LIGHTING 

312.  Tungsten,  or  Mazda,  lamps.  The  filament  in  modern 
incandescent  lamps  is  pure  metallic  tungsten,  which  has  an  ex- 
ceedingly high  melting  point,  above  3000°  C.  This  fine  metallic 
wire  is  heated  white  hot,  that  is,  to  incandescence,  by  an  electric 
current.  The  tungsten  wire  used  in  a  100- watt  lamp  is  only 
about  3  mils  (0.003")  in  diameter;  but  it  is  so  long  that  to 


352 


EFFECTS  OF  AN  ELECTRIC  CURRENT 


Fig.     350. 


get  it  into  an  ordinary  bulb  it  is  wound  zigzag  on  a  star-shaped 
reel.  The  electricity  is  led  into  and  out  of  the  filament  through 
two  short  wires  (Fig.  350),  which  are  melted  into  the  wall  of 
the  bulb  to  prevent  leakage  of  air  and  so  must  have  the 
same  coefficient  of  expansion  as  the  glass.  These  wires  are 
connected  by  copper  wires  to  the  brass  collar  and 
metal  tip  at  the  end  of  the  bulb. 

313.   Gas-filled  tungsten  lamps.     Until   recently 
it  has  been  the   practice   of   manufacturers  to   ex- 
haust the  bulbs  of  incandescent  lamps  (Mazda  B) 
to  an  almost  perfect  vacuum,  because  the  filament 
would    burn    up   at   once    if    there   were   any  air 
present  to  support  combustion.    Experiments  have 
Vacuum    shown,  however,   that  in  such  lamps  the  filament 
ttfrttda    sl°wly    vaporizes,    depositing    a     dark,    mirror-like 
B)lamp     coating  of  metal  upon  the  inside  of  the  bulb,  and  so 
in  another  type  (Mazda  C)  the  bulb  is  filled  with 
some  inert  gas,  such  as  nitrogen  or  argon.     The  presence  of 
an  inert  gas  retards  the  evaporation  of  the  filament  and  makes 
it  possible  to  operate  tungsten 
filaments   at   higher  tempera- 
tures than  in   vacuum  bulbs. 
The  long  filament  in  these  lamps 
(Mazda  C)  is  wound  into  an 
exceedingly    fine    spiral    (Fig. 
351)  and  mounted  in  a  com- 
pact form  to  prevent  its  being 
cooled  appreciably  by  the  gas. 

314.   Life  and  rating  of  incan- 
descent  lamps.     Unless    acciden-  ^—^ 

tally  broken,  Mazda  lamps  wil,  *•  *S^™^?^*A*  C> 
easily  last  1000  hours.  Such  lamps 

are  usually  grouped  in  parallel  on  a  constant-potential  circuit  of  from 
1 10  to  120  volts.  It  is  now  the  custom  of  manufacturers  to  rate  all  incan- 
descent lamps  in  watts,  and  to  specify  on  the  label  of  every  lamp  the 
voltage  at  which  it  is  designed  to  operate.  During  the  past  few  years  the 


ARC  LAMPS 


353 


lamp  manufacturers  have  repeatedly  and  rapidly  increased  the  effi- 
ciency of  the  tungsten  lamp.  Such  lamps  are  about  three  times  as 
efficient  as  the  old,  now  almost  obsolete,  carbon-filament  lamps.  The 
rate  of  consumption  of  electrical  energy  for  a  vacuum  tungsten  lamp 
is  about  1.25  watts  per  candle  power  (section  427),  depending  on  the 
size  of  the  lamp.  The  rate  for  a  gas-filled,  100-watt  lamp  for  parallel 
circuits  is  less  than  0.80  watts  per  candle  power ;  and  for  a  gas-filled 
series  lamp  for  street  lighting,  the  rate  may  be  as  low  as  0.45  watts 
per  candle  power. 

315.  The  electric  arc.  About  a  hundred  years  ago  Sir 
Humphry  Davy,  by  using  a  battery  of  2000  cells,  made  an 
electric  arc  between  rods  of  charcoal.  This  was  merely  a 
brilliant  lecture  experiment,  and  it  was  not  until  sixty  years 
later,  when  practical  generators  had  been  built,  that  arc  lights 
became  commercially  possible.  It  was  soon  found  that  the 
coke  which  is  formed  in  the  ovens  of 
gas  furnaces  makes  a  more  durable  ma- 
terial for  the  carbon  than  wood  charcoal. 

To  show  the  form  of  the  electric  arc,  we 
may  connect  a  circuit  of  50  or  more  volts 
to  two  carbons,  in  series  with  a  suitable 
rheostat.  The  light  is  so  intense  that  the 
eyes  must  be  shielded  by  blue  glass  from 
the  direct  glare.  The  arc  can  be  projected 
on  a  screen  with  a  convex  lens.  If  direct 
current  is  used,  the  crater  formed  on  the 
positive  carbon  and  the  cone  on  the  negative 
carbon  can  be  seen  (Fig.  352).  The  great- 
heat  evolved  is  shown  by  the  fact  that  iron 
wire  can  be  melted  in  the  arc. 


Fig.  352.  Positive  and 
negative  carbons  of  an 
arc. 


Furnaces  built  on  the  principle  of  the  electric  arc  are  used 
to  prepare  artificial  graphite,  carborundum,  calcium  carbide, 
and  various  kinds  of  steel. 

316.  Modern  arc  lamps.  Even  coke  carbon  burns  away, 
and  so  automatic  lamps  have  been  invented  which  feed  their 
carbons  gradually  toward  each  other.  Some  of  the  early  forms 
of  these  lamps  made  use  of  clockwork  to  feed  the  carbons ; 


354 


EFFECTS  OF  AN  ELECTRIC  CURRENT 


Ont* 


Fig.  353- 


Arc   lamp,    and   diagram  of 
automatic  feed. 


but  now  it  is  common  to  use  a  clutch  which  is  worked  by  an 
electromagnet.     One  form   of  this  mechanism  consists  of  a 

"ballasting"  resistance  B  (Fig. 
353),  which  opposes  any  in- 
crease or  decrease  of  current 
between  the  carbon  tips,  and 
of  a  "  regulating  "  coil  S,  to 
control  the  distance  between 
the  carbon  tips.  When  there 
is  no  current,  the  plunger  P 
drops  and  releases  the  friction 
clutch  on  the  upper  carbon  C. 
When  the  current  is  on,  the 
plunger  P  is  pulled  up  and 
lifts  the  clutch  and  upper  car- 
bon the  proper  distance. 

To  overcome  the  rapid 
consumption  of  carbon  rods,  an  inclosed  arc  lamp  has  come 
into  use.  When  the  arc  is  surrounded  by  a  glass  globe  which 
is  nearly  air-tight, 

the  available  SUP-  *  Starting  Resistance 

ply  of  oxygen  is 
quickly  used  up 
and  the  same  pair 
of  carbons  lasts 
100  hours  instead 
of  only  7  or  8 
hours. 

One  form  of  the 
flaming  arc  lamp 
is  the  metallic, 
or  magnetite,  arc. 
In  this  lamp  (Fig. 

354)  the  negative  electrode  is  made  of  magnetite  or   some 
similar  substance,  powdered  and  compressed  in  a  sheet-iron 


Magnetite,  etc. 


Fig.  354-     Metallic  arc  lamp  and  diagram  of  connections. 


MERCURY    ARC 


355 


tube ;  while  the  positive  electrode  is  of  solid  copper,  which 
wastes  away  very  little.  This  lamp  is  used  for  street  lighting 
on  constant-current  circuits. 

If  carbon  rods  are  used  with  a  core  of  calcium  fluoride,  the 
vapor  given  off  is  very  luminous  and  emits  light  of  a  golden 
orange  color.  These  flaming  arcs  are  used  on  streets  chiefly 
for  display  lighting.  In  this  type  the  carbons  are  long  and 
slender,  and  both  carbons  feed  down. 

In  the  mercury  arc,  or  Cooper-Hewitt  lamp,  use  is  made 
of  the  luminescence  of  mercury  vapor.  The  mercury  is 
held  in  the  lower  end  of  a  glass  vacuum  tube  2  to  4  feet 
long  (Fig.  355).  Some 
special  device  has  to  be 
used  to  start  the  current 
through  the  mercury  va- 
por ;  but  once  started,  the 
current  flows  easily  through 
the  hot  vapor,  which  glows 
with  a  light  composed  of 
green,  blue,  and  yellow, 
but  no  red.  This  gives  a 
peculiar  color  to  objects 

thus  illuminated.  (See  Rg  J55  Mercury  arc  lamp  started  by 
Chapter  XXII.)  tilting. 

QUESTIONS  AND  PROBLEMS 

1.  In  selecting  the  proper  kind  of  electric  lamp  for  illumination, 
what  other  factors  must  be  considered  besides  watts  per  candle  power  ? 

2.  How  may  a  street  car  which  is  operated  on  a  550-volt  line  be 
lighted  by  110- volt  lamps?     Draw  a  diagram  of  the  connections. 

3.  How  many  0.4-ampere  lamps,  connected   in   parallel,  can  be 
protected  by  a  20-ampere  fuse? 

4.  How  many  candle  power  should  a  50-watt  tungsten  lamp  give, 
if  it  is  rated  as  1.2  watts  per  candle  power? 

5.  The  old-type,  16-candle-power  carbon  lamp  required  55  watts, 
(a)    Compute  the  watts  per  candle  power.     (6)  If  the  lamp  itself 
cost  16  cents,  compute  the  total  cost  of  burning  it  for  1000  hours. 


356  EFFECTS  OF  AN  ELECTRIC  CURRENT 

6.  A  25-watt  Mazda  B  lamp  is  rated  as  1.17  watts  per  candle  power. 
If  the  lamp  itself  costs  27  cents  and  electricity  costs  10  cents  per  kilo- 
watt hour,  compute  (a)  the  candle  power  of  the  lamp,  and  (6)  the 
total  cost  of  burning  the  lamp  for  1000  hours. 

7.  A  gas  jet  burning  5  cubic  feet  of  gas  per  hour  gives  a  flame 
of  20  candle  power.     The  gas  costs  $1.00  per  1000  cubic  feet.      A 
40-watt  lamp  gives  about  32  candle  power.     Electricity  is  10  cents  per 
kilowatt  hour.     Compare  the  cost  of  illumination  with  gas  and  elec- 
tricity. 

8.  When  gas  is   burned  in  a  Welsbach  mantle,  it  is  generally 
consumed  at  the  rate  of  3.5  cubic  feet  per  hour  and  gives  about  70 
candle  power  of  light.     Compare  the  cost  of  illumination  with  Welsbach 
mantles  and  electricity. 

9.  One  hundred  25-watt  110-  volt  lamps  are  connected  in  parallel 
in  a  building  which  is  located  200  feet  from  the  generator.     What 
size  wire  will  be  required,  if  the  line  drop  in  the  main  feeders  is  not  to 
exceed  2  volts  ? 

10.  Why  must  a  rheostat  be  used  in  series  with  the  arc  lamp  in  a 
projection  lantern  ? 

11.  A  small  arc  lamp  needs  a  current  of  5  amperes  and  an  e.m.f.  of 
55  volts.     What  is  the  resistance  of  the  lamp  ? 

12.  If  the  lamp  in  problem  11  is  used  on  a  115-  volt  line,  what  resis- 
tance must  be  put  in  series  with  it  ? 

13.  A  certain  searchlight  requires  100  amperes  and  a  difference  of 
potential  of  60  volts.     What  resistance  must  be  placed  in  series  with 
it  on*  a  1  10-  volt  circuit  ? 

14.  If  the  arc  in  problem  13  gives  128,000,000  candle  power,  how 
many  candle  power  does  it  give  per 


PRACTICAL  EXERCISES 

1.  Report  on  the  lighting  system  of  your  city.     What  sort  of  street 
lamps  are  used?     What   service  is    supplied    for  factories?     What 
service  is  furnished  for    household  uses?     What    is  the  method  of 
distribution?     How  is  your  own  home  wired?     Where  is  the  meter 
located  ?     How  is  the  wiring  protected  by  fuses  ? 

2.  Pocket   flashlight.     Take  a   pocket-flashlight  lamp  apart  and 
examine  its  construction  carefully.     Make  a  clear  diagram  of  the 
electrical  circuit  and  explain  its  operation. 


ELECTROLYSIS  OF   WATER 


357 


CHEMICAL  EFFECTS  OF  ELECTRIC  CURRENTS 

317.  Conduction  by   solutions.     When  an  electric   current 
flows  along  a  copper  wire,  the  wire  becomes  warm  and  is  sur- 
rounded by  a  magnetic  field.     When  an  electric 

current  flows  through  a  solution  of  salt  and 
water,  the  solution  is  warmed  and  is  surrounded 
by  the  magnetic  field ;  and  it  is  at  the  same 
time  decomposed,  or  broken  up.  For  example, 
under  certain  conditions  an  electric  current  will 
decompose  salt  water  into  caustic  soda,  hydro- 
gen, and  chlorine.  Not  all  liquids  conduct  elec- 
tricity ;  thus  alcohol  and  kerosene  are  noncon- 
ductors. All  liquids  which  conduct  electricity 
and  are  more  or  less  decomposed  in  the  pro- 
cess are  called  electrolytes. 

318.  Electrolysis    of    water.     Water    (made 
slightly  acid  with  sulfuric  acid)  can  be  decomposed  by 
an  electric  current  in  the  apparatus  shown  in  figure 
356.     The  platinum  electrodes  are  connected  with 
a  battery  or  generator,  giving  at  least  5  or  6  volts. 
The  electrode  in  tube  A,  which  is  connected  to  the 
positive  (+)  pole,  is  called  the  anode;  and  the  other 

electrode  in  B  is  the  cathode.  The  current  passes  Fig.  356.  Water 
through  the  solution  from  the  anode  to  the  cathode.  is  decomposed 
Small  bubbles  of  gas  are  seen  to  rise  from  both 
electrodes,  and  the  gas  collects  in  tube  B  twice  as 
fast  as  in  tube  A.  When  tube  B  is  full,  we  open  the  switch,  and 
test  the  collected  gases.  To  test  the  gas  in  tube  B,  we  open  the 
stopcock  at  the  top  and  apply  carefully  a  lighted  match.  This  gas 
burns  with  a  pale  blue  flame,  which  shows  it  to  be  hydrogen.  If  we 
open  the  stopcock  in  tube  A  and  bring  a  glowing  pine  stick  near,  it 
bursts  into  a  flame,  which  shows  the  gas  to  be  oxygen. 

Thus  we  see  that  water  is  decomposed  by  electricity  into 
its  constituent  elements,  hydrogen  and  oxygen.  This  pro- 
cess of  decomposing  a  compound  by  means  of  an  electric  cur- 
rent  is  called  electrolysis. 


by  the  electric 
current. 


358 


EFFECTS  OF  AN  ELECTRIC   CURRENT 


319.  Theory  of  electrolysis.  The  theory  of  this  process  may  be 
stated  as  follows:  The  small  quantity  of  sulfuric  acid  (H2SO4),  when 
put  into  the  water,  breaks  up  into  hydrogen  ions  (2  H  +)  and  sulfate 
ions  (S04 ),  which  have  positive  and  negative  charges  of  electricity 
respectively.  When  the  current  is  sent  through  the  solution,  the 
positive  hydrogen  ions  (2H+)  wander  toward  the  cathode  and  the 
negative  sulfate  ions  (SO4  ~  ~)  toward  the  anode.  At  the  cathode,  the 
hydrogen  ions  give  up  their  positive  charges  and  rise  to  the  surface 
as  bubbles  of  hydrogen.  At  the  anode,  the  sulfate  ions  give  up  their 
negative  charges  of  electricity  and  react  with  the  water  (H2O)  to  form 
sulfuric  acid  (H2SO4)  and  to  set  free  oxygen  (O2).  In  this  way  the 

sulfuric  acid,  which  is  added  to  conduct 
,-  the  electricity,  is  not  used  up,  while  the 

water   (2H2O)    is   broken   into    hydrogen 

(2H2)  and  oxygen  (02). 

320.  Electroplating.  We  may  illus- 
trate the  process  of  electroplating  by 
the  following  experiment. 


Fig-  357-     Electrolysis  of  cop- 
per sulfate  solution. 


We  put  two  platinum  electrodes  in  a 
U-tube  filled  with  copper  sulfate  solution 
(CuSO4),  as  shown  in  figure  357.  After 
the  electric  current  has  passed  through 
the  solution  for  a  few  minutes,  we  find  that 

the  cathode  is  coated  with  metallic  copper,  while  the  anode  is  unchanged. 
If  we  reverse  the  direction  of  the  current,  we  find  that  copper  is  de- 
posited on  the  clean  platinum  plate,  which  is  now  the  cathode,  and 
that  the  copper  coating  on  the  anode  gradually  disappears. 

In  this  way  one  metal  can  be  coated  with  another.  For 
example,  articles  of  brass  and  iron,  which  corrode  in  the  air, 
can  be  coated  with  nickel,  which  does  not  corrode.  Similarly, 
much  cheap  jewelry  is  gold  or  silver  plated.  Many  knives, 
forks,  and  spoons  are  silver  plated,  the  best  being  what  is 
called  "  triple  "  or  "  quadruple  plate." 

In  practice  the  process  is  done  in  vats,  as  in  figure  358.  The  ob- 
jects to  be  plated  are  hung  from  one  copper  "  bus  "bar  ;  and  the  metal 
to  be  deposited,  in  this  case  pure  silver,  is  hung  from  the  other  bar. 
The  vat  contains  a  solution  of  the  metal  to  be  deposited.  For  silver 
plating  a  solution  of  silver  and  potassium  cyanide  is  used.  The 


REFINING  OF  METALS 


359 


bar  carrying  the  metal  to  be  deposited  is  con- 
nected with  the  +  terminal  of  a  low-voltage 
generator,  and  the  other  bar  to  the  —  terminal. 
The  silver  anodes  dissolve  as  fast  as  the  silver 
is  deposited  on  the  cathode,  the  strength  of 
the  solution  remaining  unchanged.  When  the 
coating  has  reached  the  proper  thickness,  a  final 
process  of  buffing  and  polishing  gives  the  sur-  Fig.  358. 
face  the  desired  appearance. 


Diagram 
electroplating  vat. 


321.  Electrotyping.     One  might  suppose  that  this  book  was 
printed  from  the  actual  type  which  was  set  up;    but  that 
is  not  the  case.     Most  books  which  are  made  in  large  numbers 
are  printed  from  electrotype  "  plates."     A  wax  impression  of 
the  page  as  set  up  in  type  is  made  in  such  a  way  that  every  letter 
leaves  its  imprint  on  the  wax  mold.     Since  the  wax  is  itself  a 
nonconductor,  it  has  to  be  coated  with  graphite.     This  mold 
is  then  placed  in  a  solution  of  copper  sulf ate  and  attached  to  the 
negative  bus  bar,  so  that  it  becomes  the  cathode,  while  a  copper 
plate  acts  as  the  anode.     After  the  current  has  deposited  copper 
on  the  wax  mold  to  the  thickness  of  a  visiting  card,  this  shell 
of  copper  is  separated  from  the  mold  and  "  backed  up  "  with 
type  metal  to  give  it  the  necessary  strength  for  printing. 

322.  Refining    of   metals.     Copper  as  it   comes  from  the 
smelting  works  is  not  pure  enough  for  some  purposes,  such 
as  making  wires  and  cables  for  carrying  electricity.     So  the 
copper  for  electrical  machinery  is  refined  by  electricity.     The 
crude  copper  is  the  anode,  a  thin  sheet  of  pure  copper  is  the 
cathode,  and  the  solution  is  copper  sulf  ate.     The  copper  de- 
posited by  the  electric  current  is  remarkably  pure.     The  anode 
of  crude  copper  gradually  dissolves,  and  the  impurities  drop  to 
the  bottom  of  the  vat  as  mud.     In  this  mud  there  is  generally 
enough  gold  and  silver  to  pay  the  expense  of  the  process.     The 
crude  copper  which  comes  from  ordinary  smelters  with  from 
two  to  five  per  cent  of  impurities  is  refined  by  electrolysis  so 
that  it  is  about  99.95  per  cent  pure  copper.     Copper  purified 
in  this  way  is  known  commercially  as  electrolytic  copper. 


360  EFFECTS   OF  AN  ELECTRIC  CURRENT 

323.  Electrochemical  equivalents  of  metals.     Experiments 
show  that  a  given  current  always  deposits  the  same  amount 
of  a  given  metal  from  a  solution  in  a  given  time.     In  fact, 
this  is  so  accurately  true  that  it  is  the  basis  of  the  most 
accurate  method  known  for  calibrating  standard  ammeters. 
The  amount  of  metal  deposited  by  a  current  depends  (1)  on 
the  strength  of  the  current,  (2)  on  the  time  it  flows,  and  (3)  on 
the  nature  of  the  metal.     The  definite  quantity  of  a  substance 
deposited  per  hour  by  electrolysis  when  one  ampere  is  flowing 
through  a  solution  is  called  the  electrochemical  equivalent  of  the 
substance. 

ELECTROCHEMICAL  EQUIVALENTS 

ELEMENT  SYMBOL  GRAMS  PER  AMPERE  HOUR 

Aluminum Al  .    ., .:.,;,. .,<,;  ;.fli. .  ,  ^ .  *.    .  0.337 

Copper   .     .    ...    .    .  Cu  .    .'.,,    .    .,    .;    .    .,,,".     .  1.186 

Gold Au .    .    .'  .    .  3.677 

Hydrogen H V   .    .     .  0.0376 

Nickel Ni 1.094 

Oxygen O 0.298 

Silver Ag 4.025 

324.  Definition  of  the  international   ampere.     Electrical  engineers 
have  agreed  to  define  the  ampere  in  terms  of  its  chemical  effect.     If  two 
silver  (Ag)  plates  are  placed  in  a  jar  of  silver  nitrate  solution  (AgNO3), 
and  if  the  +  and  —  terminals  of  a  battery  are  connected,  one  to  one 
plate  and  one  to  the  other,  it  will  be  found  that  the  plate  where  the 
current  goes  in  (the  anode)  loses  in  weight  because  silver  is  dissolved, 
and  the  plate  where  the  current  comes  out  (the  cathode)  gains  in  weight 
because  silver  is  deposited.     By  international  agreement  the  quantity 
of  electricity  which   deposits  0.001118  grams  of  silver  is  one  coulomb; 
and  the  current  which  deposits  silver  at  the  rate  of  0.001118  grams  per 
second  is  one  ampere.     The  apparatus  used  in  the  accurate  measure- 
ment of  current  by  this  method  is  shown  in  figure  359.     The  anode 
is  the  silver  disk  S  at  the  left,  and  the  cathode  is  the  silver  (or  platinum) 
cup  P  at  the  bottom.    The  porous  cup  C  at  the  right  is  put  into  the 
solution  between  the  anode  and  the  cathode  to  catch  any  mud  or  slime 
due  to  impurities  in  the  anode. 


QUESTIONS  AND  PROBLEMS 


361 


Fig.  359- 


Silver  coulomb  - 
meter. 


QUESTIONS  AND  PROBLEMS 

1.  To  determine  which  is  the  +  and  which  the  —  pole  of  a  gen- 
erator, two  copper  wires  are  sometimes  connected  to  the  terminals 
and  the  bared   ends  dipped   in   a  glass  of 

water.  One  will  soon  turn  dark.  How  does 
this  experiment  show  which  is  the  positive 
terminal  ? 

2.  How  many  grams  of  silver  are  depos- 
ited in  8  hours  from  a  silver  nitrate  solution 
by  a  current  of  5  amperes  ? 

3.  How  many  liters  of  hydrogen  will  be 
generated  by  a  current  of  10  amperes  in  4 
hours?     (A  liter  of    hydrogen  weighs  0.09 
grams  under  standard  conditions.) 

4.  How  many  amperes  will   be  needed 
to  deposit  1.5  pounds  of  copper  per  day  of 
24  hours? 

5.  How  long  will  it  take  a  current  of  200 
amperes  to  refine  a  ton  of  copper  ? 

6.  In  an  electroplating  bath  how  many  grams   of   zinc   will  be 
deposited  by  a  current  of  15  amperes  in  45  minutes? 

7.  In  calibrating  an  ammeter  the  current  was  allowed  to  run  2  hours 
and  15  minutes,  and  deposited  39.5  grams  of  silver.     What  would 
be  the  reading  of  the  ammeter,  if  correct  ? 

8.  Two  electroplating  vats  are  arranged  in  series,  one  for  gold  and 
the  other  for  silver.     How  much  gold  is  deposited  while  1  gram  of 
silver  is  being  deposited  ? 

9.  An  electroplater  buys  his   electricity  by  the  kilowatt  hour. 
The  metal  deposited  in  electroplating  is  proportional  to  the  number 
of  ampere  hours.     Why  does  he  use  as  low  a  voltage  as  possible? 

10.  What  is  meant  by  triple  and  quadruple  plate  ? 

11.  An  iron  casting  is  to  be  copper  plated  and  then  nickel  plated. 
If  the  current  used  in  each  case  is   10  amperes,  how  long  must  it 
remain  in  each  vat  to  have  8  ounces  of  each  metal  deposited  on  it? 
(1  ounce  =  28.35  grams.) 

PRACTICAL  EXERCISE 

Cleaning  silver  by  the  electrolytic  method.     Fill  an  aluminum  pan 
with  a  hot  solution  of  baking  soda  and  salt  (about  1  teaspoonful  of 


362 


EFFECTS  OF  AN  ELECTRIC  CURRENT 


each  to  a  quart  of  water).  Place  the  tarnished  silver  in  the  solution 
so  that  it  is  entirely  covered.  Keep  the  solution  boiling  a  few  minutes 
until  the  tarnish  has  been  removed.  Rinse  the  silver  in  clean  water 
and  wipe  with  a  soft  cloth.  For  an  explanation  of  the  chemical  action 
involved,  read  page  432  Black  and  ConanCs  Practical  Chemistry  (Mac- 
millan).  This  method  does  not  apply  to  plated  ware. 


STORAGE  BATTERIES 

325.  What  is  a  storage  battery  ?  Some  people  think  of  a  storage 
battery  as  a  sort  of  condenser  where  electricity  is  stored  ;  but  it 
is  not  that.  In  the  storage  battery,  as  in  any  other  battery, 
the  electrical  energy  comes  from  the  chemical  energy  in  the  cells. 
The  charging  process  consists  in  forming  certain  chemical  sub- 
stances by  passing  electricity  through  a  solution,  just  as  hydro- 
gen and  oxygen  are  formed  in  the  electrolysis  of  water.  In 

the  discharging  process,  elec- 
tricity is  produced  by  the  chem- 
ical action  of  the  substances 
which  have  been  formed  in  the 
charging  process. 

326.  Lead  storage  cell.     We 

may  make  a  small  lead  storage  cell 
by  putting  two  sheets  of  ordinary 
lead  in  a  glass  battery  jar  with  a 
very  dilute  solution  of  sulfuric  acid. 
To  charge  it  or  "  form  "  the  plates 
quickly,  we  connect  this  cell  and 
an  ammeter  in  series  with  a  battery 
of  three  or  more  cells  ;  or  better,  a 
generator  of  about  6  volts  (Fig. 
360).  While  the  current  is  passing, 
bubbles  of  gas  rise  from  each  plate. 
If,  after  a  few  minutes,  we  disconnect 

the  generator  and  touch  the  wires  of  a  voltmeter  to  the  lead  termi- 
nals, it  shows  an  e.m.f.  of  about  2  volts.  If  we  then  connect  an 
electric  bell  in  series  with  the  ammeter  and  the  lead  cell,  the  bell  rings. 
This  indicates  that  a  current  is  produced ;  and  the  ammeter  shows  that 
the  current  on  discharge  is  opposite  to  that  used  in  charging  the  cell. 


Fig.  360.  Forming  a  lead  storage  cell. 


THE    LEAD    STORAGE    BATTERY 


363 


Sand 


When  the  plates  are  lifted  out  of  the  solution 
after  charging,  plate  B,  the  anode,  is  brown, 
because  of  a  coating  of  lead  peroxide  (Pb02) ; 
and  plate  A,  the  cathode,  is  the  usual  gray  of 
pure  lead  (Pb). 

In  the  commercial  lead  storage  cell 
(Fig.  361),  the  negative  plates  are  pure 
spongy  lead  (Pb),  the  positive  are  lead 
peroxide  (Pb02),  and  the  electrolyte  is 
dilute  sulfuric  acid.  In  the  charging 
process,  the  positive  plate,  which  is  dark 
brown,  is  coated  with  lead  peroxide,  and 
the  negative,  which  is  gray,  is  made  into 

i       -i       -r     ,1        vv         •  Fig.  361.     Glass  jar  of  a 

spongy  lead.     In  the  discharging  process,       storage  cell  suppol:ted 

both  plates  gradually  return  to  a  condi-       on  sand. 

tion   where    each   is   covered   with   lead 

sulfate    (PbS04).     The    chemistry   of   these    changes   can  be 

briefly  described  by  the  following  equation : 

-< — Charge 

Pb02  +  Pb  +  2  H2SO4  =  2  PbSO4  +  2  H20. 
Discharge — >• 

It  will  be  noticed  that  during  the  charging  process  the  acid 
becomes  more  concentrated.  So  the  condition  of  a  storage 
cell  can  be  determined  by  the  specific  gravity  of  the  acid. 
The  plates  in  the  commercial  lead  battery  are  either  roughened 
and  then  changed  into  the  proper  active  materials,  lead  peroxide 
and  spongy  lead,  by  a  chemical  process,  or  are  punched  full  of 
holes  which  are  filled  with  the  active  material. 

327.  Uses  of  the  storage  battery.  The  most  familiar  form  of 
storage  battery  is  doubtless  that  used  on  automobiles  for  starting, 
lighting,  and  ignition.  Such  a  battery  (Fig.  362)  usually  consists  of 
3  cells  (6  volts)  or  6  cells  (12  volts),  and  has  a  capacity  of  from  60  to 
80  ampere  hours  (see  section  328).  Since  the  majority  of  automobile 
owners  are  careless  about  giving  the  battery,  which  is  the  heart  and 


364 


EFFECTS  OF  AN  ELECTRIC   CURRENT 


center  of  the  starting  and  lighting  system,  the  attention  it  should 
have,  these  batteries  have  to  be  built  for  abuse  as  well  as  for  use. 

Very  large  storage  batteries  are  used  in  connection  with  central 
power  stations  to  regulate  the  load  by  helping  to  carry  the  "  peak  " 
loads,  and  to  serve  as  reserve  power  to  be  used  in  case  of  emergency. 
Large  storage  batteries  are  used  on  submarine  boats;  for  while  the 
boat  is  submerged,  it  is  wholly  dependent  for  power  on  its  batteries. 


Expansion    Fillet 
Chamber 


Mud  Spaces' 

Fig.  362.    Automobile  battery  and  section  of  one  cell. 

Storage  batteries  are  also  used  for  train  lighting  and  are  in  this  case 
charged  from  an  axle-driven  generator.  There  is  a  rapidly  growing 
field  of  usefulness  for  the  storage  battery  in  vehicle  service,  both  for 
pleasure  carriages  and  for  heavy  trucks. 

There  are  many  other  important  uses  of  the  storage  battery,  in 
radio  telegraphy  and  radio  telephony,  for  private  lighting  plants  where 
the  service  of  a  central  station  is  not  available,  for  telephone  exchanges 
and  telegraph  circuits,  for  fire-alarm  and  signal  systems,  and  in  test- 
ing laboratories  where  a  constant  voltage  is  necessary. 

328.  Testing  a  battery.  As  yet  no  one  has  invented  a 
"  fool-proof  "  storage  battery.  It  requires  continual,  intelli- 
gent oversight,  just  like  any  other  delicate  piece  of  machinery. 
We  may  test  a  dry  cell  very  easily  with  a  pocket  ammeter ;  but 
if  we  try  the  same  method  with  a  storage  battery,  we  instantly 
burn  out  the  instrument.  This  happens  because  the  internal 
resistance  of  the  battery  is  exceedingly  small,  and  accord- 
ingly the  current  which  flows  through  the  ammeter  is  enor- 
mous. 


EDISON  STORAGE   BATTERY  365 

The  voltage  of  a  storage  cell  is  about  2  volts.  Nevertheless  it 
should  be  remembered  that  the 'voltage  of  a  cell  on  open  circuit 
tells  us  absolutely  nothing  about  its  condition  as  to  charge  and  dis- 
charge. The  voltage  must  always  be  measured  during  the 
process  of  charging  or  discharging  at  its  normal  rate.  Cells 
may  be  fully  charged  up  to  about  2.5  volts.  The  discharge 
should  be  stopped  when  the  terminal  voltage  has  dropped 
to  about  1.8  volts  at  normal  rate  of  discharge.  Storage  cells 
are  sold  according  to  their  capacity  in  ampere  hours,  and  this 
rating  is  based  on  a  steady  discharge  for  8  hours.  Thus,  an  80- 
ampere-hour  battery  would  maintain  a  current  of  10  amperes 
for  8  hours,  and  so  10  amperes  would  be  its  normal  rate  of 
discharge. 

The  amount  of  charge  in  a  battery  is  best  determined  by  measur- 
ing the  specific  gravity  of  the  electrolyte  by  means  of  a  hydrometer. 
The  specific  gravity  of  the  acid  used  depends  on  the  type  of  bat- 
'tery  and  its  intended  service.  For  portable  automobile  bat- 
teries, the  solution  should  have  a  specific  gravity  of  1.27  to  1.29 
when  fully  charged,  and  it  will  be  from  1.15  to  1.17  when  com- 
pletely discharged.  The  manufacturers  furnish  careful  direc- 
tions for  the  use  and  care  of  their  batteries. 

329.  Care  of  a  battery.     Among  the  most  important  points  to  bear 
in  mind  are  the  following : 

(1)  Test  each  cell  with  a  hydrometer  every  two  weeks. 

(2)  Keep  the  plates  covered  with  liquid.     Add  only  distilled  water. 

(3)  In  charging,  connect  the  positive  terminal  of  the  power  supply 
to  the  +  terminal  of  the  battery,  and  use  only  direct  current. 

(4)  Do  not  short-circuit  the  terminals  of  a  battery. 

(5)  Keep  all  connections  clean  and  bright. 

(6)  An  idle  battery  will  not  remain  charged,  but  must  have  atten- 
tion at  least  once  a  month. 

330.  Edison  storage  battery.     The  great  objections  to  the 
lead  storage  battery  are  its  weight,  its  expense,  and  its  need  of 
close  supervision.     Edison  has  invented  a  storage  cell  in  which 
the  negative  plate  is  pure  iron  in  a  steel  frame,  the  positive; 
plate  is  nickel  peroxide,  and  the  solution  is  caustic  soda. 


366 


EFFECTS  OF  AN  ELECTRIC   CURRENT 


If  a  current  is  drawn  from  this  battery  (Fig.  363),  the  nickel  peroxide 
(Ni02)  is  reduced  to  a  lower  oxide  (Ni203),  while  the  iron  is  oxidized 
to  form  FeO.  This  action  is  reversed  on  charging,  as  will  be  seen  in 
the  following  chemical  equation : 


-< Charge 

2  Ni02  +  Fe  =  Ni203  + 
Discharge >• 


FeO 


It  will  be  noted  that  the  electrolyte  does  not  appear  in  this  equation 
at  all.  The  change  in  its  density  is  therefore  so  slight  that  it  is 
insufficient  to  indicate  the  condition  of  the  cell. 


Fitter  Cap      Positive  Pole 


Negative  Grid 
with   . — 
Iron  Oxide 


Positive  Grid 

urith 

Nickel  Hydrate 
and 


Since  this  cell  is 
intended  for  trac- 
tion work,  great 
pains  have  been 
taken  to  make  it 
light,  strong,  and 
compact.  Instead 

Nickel  in  Layers    Qf   being   placed    in 

a  glass  or  hard- 
rubber  tank,  it  has 
a  thin  nickel- 
plated,  sheet-steel 
case.  In  a  lead  cell 
the  normal  voltage 
on  discharge  is  2 
volts  ;  in  the  Edison 
cell  it  is  1.2  volts. 
For  the  same  ca- 
pacity of  output, 
the  Edison  cell  is 
about  half  as  heavy 
as  the  lead  cell.  As  the  internal  resistance  of  the  Edison 
is  a  little  more  than  that  of  the  lead  cell,  its  efficiency  is  a 
little  lower. 


Fig.  363- 


Side 

Insulator 

Edison   storage    cell  with  side  partly  cut 
away  to  show  construction. 


PROBLEMS  367 

PROBLEMS 

1.  A  lead  cell  has  an  e.m.f .  of  2.00  volts,  and  its  internal  resistance 
is  0.004  ohms.     What  will  be  its  terminal  voltage  when  discharging 
25  amperes? 

2.  What  would  be  the  impressed  voltage  needed  to  charge  the  cell 
of  problem  1  at  the  rate  of  25  amperes  ? 

3.  What  would  be  the  terminal  voltage  of  the  cell  in  problem  1 
when  discharging  at  the  rate  of  50  amperes  ? 

4.  If  the  e.m.f.  of  a  lead  cell  is  2.3  volts  on  open  circuit,  while 
the  terminal  voltage  when  the  cell  is  delivering  10  amperes  is  only  2 
volts,  what  is  the  internal  resistance  of  the  cell? 

6.  A  battery  of  24  lead  storage  cells  in  series,  each  having  an  e.m.f. 
of  2.1  volts,  a  normal  charging  rate  of  15  amperes,  and  an  internal 
resistance  of  0.005  ohms,  is  to  be  charged  by  a  generator.  What  must 
be  the  terminal  voltage  of  the  generator? 

6.  In  a  trolley  system  the  generator  maintains  565  volts  on  the 
line.     How  many  lead  storage  cells  in  series,  each  of  2.1  volts,  will  be 
needed  to  help  the  generator  carry  the  peak  of  the  load  ? 

7.  Most  manufacturers  of  lead  cells  allow  about  55  ampere  hours 
for  each  square  foot  of  positive  plate  area.     How  large  a  plate  area 
will  be  required  in  problem  2  ? 

8.  A  storage  battery  is  used  to  light  20  incandescent  lamps,  each 
requiring  0.4  amperes  at  112  volts.     How  many  cells,  each  having  an 
e.m.f.  of  2  volts  and  an  internal  resistance  of  0.004  ohms,  will  be 
needed  ? 

9.  How  many  Edison  storage  cells  of  type  B-2  are  needed  to  light 
10  incandescent  lamps  which  are  connected  in  parallel?     Each  lamp 
requires  0.4  amperes.     This  type  of  cell  has  a  capacity  of  40  ampere 
hours  when  discharging  at  its  normal  rate  of  7.5  amperes  and  gives 
1.2  volts  per  cell  at  this  discharge  rate. 


PRACTICAL  EXERCISE 

Report  on  a  storage-battery  service  station.  Visit  a  service  station 
in  your  neighborhood  and  find  out  how  cells  are  charged,  and  how 
their  condition  is  tested.  Describe  all  the  instruments  used.  Ex- 
amine a  "  sick  "  battery  which  has  been  taken  apart.  Why  is  the 
life  of  an  automobile  storage  battery  so  short? 


368  EFFECTS  OF  AN  ELECTRIC  CURRENT 

SUMMARY  OF  PRINCIPLES  IN   CHAPTER  XVI 

Lines  of    magnetic  force  around  a  straight  current  are   con- 
centric circles. 
Thumb  rule  for  straight  wire:   use  right  hand.     Thumb  points 

with  current.     Fingers  curl  with  magnetic  flux. 
Lines  of  force  around  a  coil  mostly  go  through  inside  and  come 

back  outside. 
Thumb  rule  for  coil :   use  right  hand.     Thumb  points  toward 

N-pole.     Fingers  curl  with  current. 
Power  delivered  to  circuit  =  intensity  of  current  X  voltage. 

Watts  =  amperes  X  volts. 
1  horsepower  =  746  watts. 
Electrical  energy  is  measured  commercially  in  kilowatt  hours : 

equals  kilowatts  X  hours. 
Power  used  to  overcome  resistance 

=  current  squared  X  resistance. 
Watts  =  (amperes)2  X  ohms. 
Joule  is  a  watt  second. 

Energy  in  joules  =  I2Rt 
Heat  in  calories  =  0.24  I2Rt 
Weight  of  a  substance  deposited  by  a  current 

=  electrochemical  equivalent  X  current  X  time. 
Lead  storage  cells :   Positive  plate,   lead  peroxide ;   electrolyte, 
sulfuric  acid ;   negative  plate,  spongy  lead. 
Action  on  charge  and  discharge : 

-< — Charge 
PbO2  +  2  H2SO4  +  Pb  =  2  PbSO4  +  2  H2O. 

Discharge >• 

Edison  storage  cell :    Positive  plate,  nickel  peroxide ;  electro- 
lyte, solution  of  caustic  soda  ;    negative  plate,  iron. 
Action  on  charge  and  discharge : 

•< — Charge 

2  NiO2  +  Fe  =  Ni2O3  +  FeO. 
Discharge — >- 


QUESTIONS  369 

QUESTIONS 

1.  Is  the  magnetism  created  by  an  electric  current  in  any  way 
different  from  the  magnetism  of  a  magnetized  steel  bar  ? 

2.  Why  is  an  ammeter  more  likely  to  be  injured  than  a  volt- 
meter ? 

3.  Why  do  we  test  a  dry  cell  with  a  30-ampere  ammeter  but  do 
not  so  test  a  storage  battery? 

4.  Why  does  a  test  with  an  ammeter  give  a  better  indication  of  the 
condition  of  a  used  dry  cell  than  a  test  with  a  voltmeter? 

6.  Which  will  yield  more  heat  for  warming  an  electric  car,  a 
50-ohm  resistance  connected  across  a  50-volt  line,  or  a  100-ohm  re- 
sistance connected  across  a  100-volt  line? 

6.  Compare  the  cost  per  hour  of  running  a  55-ohm  electric  heater 
on  a  55- volt  circuit  and  on  a  110- volt  circuit,  if  power  costs  10  cents 
per  kilowatt  hour. 

7.  If  electricity  is  more  expensive  than  gas  for  lighting,  why  is 
electricity  so  commonly  used? 

8.  Why  can  you  not  charge  a  lead  storage  cell  from  a  dry  cell  ? 

9.  What  is  the  advantage  of  electrotype  plates  over  the  original 
type  in  printing  a  book  ? 

10.  How  would  you  test  the  state  of  charge  or  discharge  of  an 
Edison  cell? 

11.  What  precautions  must  be  taken  in  using  an  electric  flatiron? 

12.  If  the  current  on  a  given  line  is  doubled,  how  is  the  power  loss 
due  to  heat  increased  ? 

13.  Make  a  list  of  ten  "  Don'ts  "  in  the  use  and  care  of  a  lead 
storage  battery. 


CHAPTER  XVII 


INDUCED   CURRENTS 

Currents  induced  by  magnets  —  Lenz's  law. 

The  generator  —  wire  cutting  lines  of  magnetic  force  — 
amount  and  direction  of  induced  e.m.f.  —  Fleming's  rule  — 
revolving  loop  —  commutator  —  Gramme  ring  and  drum 
armatures  —  field  excitation. 

The  motor  - —  side  push  on  wire  carrying  current  —  motor 
rule  for  direction  of  push  —  forms  of  commercial  motors  — 
back  e.m.f.  —  starting  box  —  applications  —  efficiency. 

Other  applications  of  induced  currents  —  induction  by 
electromagnets  —  induction  coils  —  automobile  ignition  — 
self-induction  —  make-and-break  spark  coils  —  the  telephone. 

331.  Faraday's  discovery.  If  we  had  to  depend  on  batteries 
for  all  of  our  electric  currents,  we  should  not  be  lighting  our 
streets  and  houses  with  electric  lamps  or  riding  on  electric  cars. 
The  cost  of  zinc  as  a  fuel  in  the  voltaic  cell  makes  the  battery 
too  expensive  as  a  source  of  large  quantities  of  electricity. 

About  1831,  both  Faraday  and  Henry  discovered  that  it  is 
possible  to  transform  mechanical  energy  directly  into  electrical 
energy.  Their  method  of  producing  electric  currents  by 
means  of  magnets  is  the  underlying  prin- 
ciple of  the  commercial  generator,  which 
has  made  possible  the  modern  age  of 
electricity. 

332.   Current  induced  by  magnets,   if  we 

connect  the  ends  of  a  coil  of  many  turns  of  fine 
insulated  wire  to  a  lecture-table  galvanometer, 
and  then  quickly  move  the  coil  down  over  one 
Fig.  364.    A  coil  moving   pole  of  a  strong  horseshoe  magnet,  as  shown  in 


downward  in  a  mag- 
netic field  generates  a 
current  as  shown. 


figure    364,    we   observe   a    deflection.     When 
we  again  raise  the  coil,,  we  observe  a  deflection 
in  the  opposite  direction.     If  we  now  lower  the 
370 


THE  GENERATOR  371 

coil  and  hold  it  down,  we  find  that  the  galvanometer  pointer  comes 
back  to  zero.  If  we  repeat  the  experiment,  moving  the  coil  down  slowly 
and  up  slowly,  we  find  that  the  deflection  is  less  than  before. 

Such  experiments  show  that  it  is  possible  to  produce 
momentary  electric  currents  without  a  battery.  An  electric 
current  produced  by  moving  a  coil  in  a  magnetic  field  is  called 
an  induced  current.  It  is  evident  from  the  experiment  that 
the  current  is  induced  only  when  the  wire  is  moving  and  that 
the  direction  of  the  current  is  reversed  when  the  motion 
changes  direction.  Since  an  electric  current  is  always  made 
to  flow  by  an  electromotive  force,  the  motion  of  a  coil  in  a 
magnetic  field  must  generate  an  induced  electromotive  force. 

333.  Direction  of  induced  currents.     If  we  take  the  same  appa- 
ratus (Fig.  364)  and  move  the  coil  down  over  the  JV-pole  of  the  magnet 
and  then  down  over  the  £-pole,  we  find  that  the  deflections  are  in 
opposite  directions  in  the  two  cases.     To  determine  in  which  direction 
the  induced  current  is  flowing  in  the  coil,  one  may  make  a  little  voltaic 
cell  by  putting  in  one's  mouth  a  copper  wire  and  a  zinc  wire  connected 
to  the  galvanometer.     Since  we  know  that  the  copper  is  the  positive 
electrode,  we  can  compare  the  direction  of  the  galvanometer  deflection 
caused  by  the  cell  current  with  that  caused  by  the  induced  current, 
and  so  determine  the  direction  of  the  latter.     In  this  way  we  find  that 
when  the  coil  is  moving  down  over  the  TV-pole  of  the  magnet,  the  in- 
duced current  is  in  such  a  direction  that  the  lower  face  of  the  coil  is  an 
N-pole.      In  a  similar  way  we  find  that  when  the  coil  is  brought  down 
over  the  $-pole  of  the  magnet,  the  induced  current  is  in  such  a  direction 
that  the  lower  face  of  the  cojl  is  an  $-pole.     In  both  cases  the  lower 
face  of  the  coil  is  a  pole  of  such  a  sort  as  to  be  repelled  by  the  pole  to- 
ward which  it  is  moving. 

The  direction  of  induced  currents  may  be  stated  as  fol- 
lows :  An  induced  current  has  such  a  direction  that  its  magnetic 
action  tends  to  resist  the  motion  by  which  it  is  produced.  This 
is  known  as  Lenz's  law. 

THE  GENERATOR 

334.  The  importance  of  the  generator.     The  most  useful 
application  of  induced  currents  did  not  come  until  nearly 
forty  years  after  Faraday  and  Henry  made  their  wonderful 


372 


INDUCED  CURRENTS 


discovery.  Then  the  generator  was  developed,  by  means  of 
which  the  enormous  energy  of  steam  engines  and  water 
wheels  can  be  transformed  into  electricity.  The  electricity 
generated  in  this  way  can  be  transmitted  many  miles.  It 

can  be  used  in  motors  to  turn 
all  sorts  of  machinery,  in  lamps 
of  various  kinds  to  light  our 
streets  and  homes,  in  heaters 
to  warm  cars  and  sometimes 
houses,  and  in  furnaces  to  melt 
iron  and  steel.  Thus  the  gen- 
erator has  revolutionized  mod- 


365.    Induced    e.m.f.   in 
cutting  lines  of  force. 


a  wire 


ern    industry     by    furnishing 
cheap  electricity. 

335.  Wire  cutting  lines  of  magnetic  force.    A  simple  way 
to  get  at  the  fundamental  idea  of  the  generator  is  to  think, 
as  Faraday  did,  of  the  induced  e.m.f.  produced  in  a  single 
wire  when  it  is  moved  across  a  magnetic  field.     Suppose  the 
straight  wire  AB  is  pushed  down  across  the  magnetic  field 
shown  in  figure  365.     An  induced  e.m.f.  is  set  up  in  AB, 
which  makes  B  of  higher  potential  than  A,  as  can  be  shown 
by  connecting  B  and  A  with  a  voltmeter.     As  long  as  the  wire 
remains  stationary  no  current  flows.     Even  if  the  wire  does 
move,  if  it  be  in  a  direction  parallel  to  the  lines  of  force,  no 
current  flows.     In  short,  a  wire  must  move  so  as   to  cut  lines 
of  magnetic  force,  in  order  to  have  an  e.m.f.  induced  in  it. 

336.  Direction  of  induced  e.m.f.     We  have  just  seen  that 
when  the  wire  AB  in  figure  365  is  moved  down,  the   induced 
current  in  it  is  from  A  to  B.     If  the  wire  were  moved  up,  the 
induced  current  would  be  from  B  to  A.     Furthermore,  if  the 
field  is  reversed  without  changing  the  direction  of  motion  of 
the  wire,  the  current  reverses.     It  will  be  seen,  then,  that  the 
direction  of  the  induced  e.m.f.  depends  upon  two  factors,  (a) 
the  direction  of  the  motion  of  the  wire,  and  (6)  the  direction  of 
the  flux,  or  magnetic  lines  of  force.     The  relation  of  these  three 


AMOUNT  OF  INDUCED   E.M.F. 


373 


directions  may  be  kept  in  mind  by  Fleming's  rule  of  three 
fingers,  as  shown  in  figure  366. 

FLEMING'S  RULE.  Extend  the  thumb,  forefinger,  and  center 
finger  of  the  right  hand  so  as  to  form  right  angles  with  each  other. 
If  the  thumb  points  in  the  direction  of  the 
motion  of  the  wire,  and  the  forefinger  in 
the  direction  of  the  magnetic  flux,  the 
center  finger  will  point  in  the  direction  of 
the  induced  current. 

To  remember  this  rule,  notice  the 
corresponding  initial  letters  in  the  words 
"fore"  and  "flux,"  "center"  and 
"  current  "  Fig-  366-  RiKht-hand  role 

for  induced  e.m.f. 

337.  Amount  of  induced  e.m.f.  If  we  have  a  large  electromagnet 
with  flat-faced  pole  pieces  (Fig.  367),  we  can  demonstrate  the  various 
laws  about  induced  currents  in  a  conductor.  If  we  move  a  wire  down 
through  the  gap  between  the  pole  pieces,  a  milli voltmeter  will  show 
the  induced  current.  If  we  hold  the  wire  at  rest  in  the  gap,  we  observe 
no  current.  If  we  move  the  wire  horizontally,  parallel  to  the  lines  of 
magnetic  flux,  we  get  no  current.  If  we  move  the  wire  up  through  the 
gap,  we  observe  a  current  in  the  opposite  direction,  as  predicted  by 

Fleming's  rule.  If  we  in- 
crease the  magnetic  field  by 
increasing  the  current  through 
the  electromagnet,  we  in- 
crease the  induced  current. 
If  we  move  the  wire  more 
quickly  through  the  gap,  we 
increase  the  induced  current. 
Finally,  if  we  bend  the  wire 
into  a  loop  of  several  turns, 
and  move  the  loop  down  over 


Fig.  367. 


Electromagnet  for  demonstrating 
induced  e.m.f. 


one  pole  so  that  all  the  wires  on  one  side  of  the  loop  pass  through  the 
gap,  we  find  that  the  current  is  increased. 

In  this  experiment  we  see  that  the  induced  e.m.f.  is  in- 
creased by  moving  the  wire  faster  across  the  magnetic  field, 
by  making  the  magnetic  field  stronger,  and  by  using  more 


374 


INDUCED  CURRENTS 


Fig.  368. 


Single  loop  of  wire  turning  in  a  mag- 
netic field. 


turns  of  wire.  In  short,  the  amount  of  induced  e.m.f.  depends 
on  three  factors :  (1)  the  speed;  (2)  the  magnetic  field ;  and  (3)  the 
number  of  turns. 

Induced  e.m.f.  varies  as  speed  X  flux  X  turns. 

338.  Commercial  generators.     A  machine  for  converting  me- 
chanical energy  into  electrical  energy  is  called  a  generator.     Its 

essential  parts  are  two : 
(1)  the  magnetic  field, 
which  is  produced  by 
permanent  magnets, 
as  in  the  magneto,  or 
by  electromagnets,  as 
in  larger  generators, 
and  (2)  a  moving  coil 
of  copper  wire,  called 
the  armature,  wound 
on  a  revolving  iron  ring  or  drum.  The  armature  wires  corre- 
spond to  the  moving  wires  in  the  experiments  above. 

339.  Current  in  a  revolving  loop  of  wire.     If  we  rotate  a  rec- 
tangular coil  between  the  poles  of  a  large  horseshoe  magnet,  or  better,  of 
an  electromagnet,  we  can  detect  an  electric  current  in  the  revolving 
coil  by  connecting  it  with  flexible   leads  to  a  galvanometer.     As  we 
turn  the  coil,  the  current  is  reversed  every  half-revolution. 

It  will  help  us  to  understand  just  what  is  happening  in  the 
revolving  coil  if  we  first  consider  what  would  happen  in  a  single 
loop  of  wire  which  is  rotated  in  a  magnetic  field,  as  shown  in 
figure  368.  If  we  start  with  the  plane  of  the  loop  vertical  and 
turn  the  handle  in  a  clockwise  direction,  the  wire  BC  moves 
down  during  the  first  half-turn ;  and  so,  by  Fleming's  rule,  we 
should  expect  the  induced  e.m.f.  to  tend  to  send  the  current 
from  C  to  B.  At  the  same  time  the  wire  AD  is  moving  up, 
and  the  current  will  tend  to  flow  from  A  to  D.  The  result  is 
that  during  the  first  half -turn  the  current  goes  around  the  loop 
in  the  direction  ADCB.  During  the  second  half -turn  the 
current  is  reversed  and  goes  around  in  the  direction  A  BCD. 


CURRENT  IN  A   REVOLVING  LOOP  OF  WIRE        375 


To  prove  that  this  really  does  happen  in  the  loop,  we  can  cut 
the  wire  and  connect  the  ends  to  slip  rings  x  and  y,  as  in  figure 
369.  The  brushes  B'  and  B",  which  rest  on  the  rings,  are  con- 
nected to  a  milliammeter.  In  this  way  it  can  be  shown  that 


Fig.  369.     Coil  rotating  between  poles  of  electromagnet,  and  diagram  of  single 
loop  connected  to  slip  rings. 

there  is  generated  in  the  coil  an  alternating  current  which 
reverses  its  direction  twice  in  every  revolution.  Moreover,  it  is 
possible  to  show  that  the  induced  e.m.f.  starting  at  zero  goes  up 
to  a  maximum  and  then  back  to  zero  in  the  first  half -turn ; 
then  it  reverses  and  goes  to  a  maximum  in  the  opposite  di- 
rection, and  finally  back  to  zero.  The  induced  e.m.f.  reaches 
its  maximum  when  the  coil  is  horizontal,  because  in  this  position 
the  wires  AD  and  BC  are  cutting  lines  of  force  most  rapidly. 
This  is  illustrated  by  the  curve  in  figure  370.  A  complete 
revolution  of  the  loop 
(360  °)  makes  a  curve, 
including  a  maximum 
in  one  direction  and  | 
the  following  maxi-  g-' 
mum  in  the  opposite 
direction.  This  is 
called  a  cycle  of  cur- 
rent. 

Machines  which  are  built  to  deliver  alternating  currents  are 
called  alternating-current  (a-c.)  generators  or  alternators. 


+30 
5+20 
3  +  10 
3      0 
n'-lO 

j~ 

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^ 

\ 

_ 

/ 

S_ 

f 

\ 

/ 

/ 

—9 

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_\ 

-y 

7 

/. 

g- 

\ 

/ 

Ss 

,/ 

pn 

SIT 

ON 

OF 

1  0 

OP 

IN 

npr 

RF 

FS 

Fig.  370. 


Curve  to  show  relation  of  induced  e.m.f. 

to  position  of  loop. 


376 


INDUCED  CURRENTS 


340.  Commutator.  To  get  a  direct  current,  that  is,  one  which 
flows  always  in  the  same  direction,  we  have  to  use  a  commutator. 
To  understand  how  this  works,  let  us  study  a  very  simple  case. 
If  the  ends  of  the  loop  in  section  339  are  connected  to  a  split 

ring,  as  shown  in  figure  371, 
we  may  set  the  brushes  B+ 
and  B—  on  opposite  sides 
of  the  ring,  so  that  each 
brush  will  connect  first  with 
one  end  of  the  loop  and  then 
with  the  other.  By  prop- 
erly adjusting  the  brushes, 
so  that  they  shift  sections 


B+ 

Fig.  371.     Split-ring  commutator. 


on  the  commutator  just 
when  the  current  reverses  in  the  loop,  that  is,  when  the  loop  is 
in  a  vertical  position,  we  may  get  the  current  to  flow  only  out 
at  one  brush  B+,  and  only  in  at  the  other  brush  B-.  The 
direction  of  the  current  in  the  external  circuit  is  always  the 
same,  even  though  the  current  in  the  loop  itself  reverses  twice 
in  every  revolution. 

The  current  delivered  by  such  a  machine  can  be  represented 
by  the  curve  in  figure  372.  Although  it  is  always  in  the  same 
direction,  it  is  pulsating. 

A  machine  with  a   commutator  for  delivering    direct    cur- 
rent is  called  a  direct- 
current  (d-c.)  gener- 
ator. 

341.  Generators  of 
steady  currents.  The 
e.m.f.  produced  by 
rotating  a  single  loop  Fig.  372. 
in  a  magnetic  field 
can  be  raised  by  using  many  turns  of  wire  and  by  rotating  the 
coil  very  fast.  Nevertheless  the  current  will  be  pulsating,  and 
this  is  unsatisfactory  for  many  purposes.  To  get  a  machine  to 


£+10 
•=    o 


00- 


POSITION   OF  LOOP    IN  DEGREES 


Curve  showing  pulsating  e.m.f.  delivered 
by  loop  fitted  with  commutator. 


GENERATORS  OF  STEADY   CURRENTS 


377 


deliver  a  steady  current,  a  Frenchman,  named  Gramme,  in- 
vented in  1870  the  so-called  Gramme-ring  form  of  armature. 

The  Gramme-ring 
armature  is  now  very 
seldom  used,  but  it  is 
worth  studying  carefully 
because  the  fundamental 
principles  of  its  action 
can  be  understood  from 

Very    simple      diagrams  ;       Fi£-  373-     Magnetic  field  in  a  Gramme  ring. 

whereas  most  armatures  of  the  common  or  drum  type,  although 
based  on  exactly  the  same  principles,  cannot  be  represented 
by  simple  diagrams. 

A  rotating  soft-iron  ring  or  hollow  cylinder  is  mounted  be- 
tween the  poles  of  an  electromagnet,  as  in  figure  373.  The 
ring  serves  to  carry  the  flux  across  from  one  pole  to  the  other. 
There  are  scarcely  any  lines  of  force  in  the  space  inside  the 
ring.  A  continuous  coil  of  insulated  copper  wire  is  wound  on 
the  ring,  threading  through  the  hole  at  every  turn.  When 
the  ring  rotates,  as  in  figure  374,  the  wires  on  the  outside  are 

cutting  lines  of  force,  but 
those  inside  are  not.  Fur- 
thermore, according  to  the 
right-hand  rule,  the  outside 
wires  on  the  right-hand  side 
are  moving  in  such  a  direc- 
tion that  the  induced  cur- 
rent tends  to  flow  toward  us. 
The  wires  lying  on  the  other 

Fig.    374-     Induced  current  in  a  coil  on  a    side   of   the   ring   are  moving 
Gramme  ring  rotating  in  a  magnetic  field. 


so  as  to  induce  a 
away  from  us.  If  there  were  no  outside  connections,  these  two 
opposing  e.m.f.'s  would  just  balance,  and  no  current  would 
flow.  This  would  be  like  arranging  a  number  of  cells  in  series 
with  an  equal  number  turned  so  that  they  are  opposed  to  the 


378 


INDUCED  CURRENTS 


r\  r\ 
\ 


£-* 


fa) 


(*) 


Fig.   375.     Opposing   batteries   (a)    without, 
and  (b)  with  an  external  circuit. 


first  group  (Fig.  375  (a)) ; 
obviously  no  current  would 
flow. 

But  if  we  imagine  the 
copper  wires  on  the  outer 
surface  of  the  ring  to  be 
scraped  bare,  and  if  two 
metal  or  carbon  blocks  or 
brushes  at  the  top  and 
bottom  rub  on  the  wires 
as  they  pass,  a  current 
could  be  led  out  of  the  armature  at  one  brush,  and,  after 
passing  through  an  external  resistance,  such  as  a  lamp,  could 
be  led  back  to  the  armature  again  at  the  other  brush.  In 
this  case  the  armature  circuit  is  double,  consisting  .of  its  two 
halves  in  parallel.  It  is  like  adding  an  external  circuit  to  the 
arrangement  of  cells  described  above.  This  battery  analogue 
for  a  Gramme-ring  armature  is  shown  in  figure  375  (6). 

In  the  Gramme-ring  arrangement  there  are  at  every  instant 
the  same  number  of  active  conductors  in  each  half  of  the  arma^ 
ture  circuit,  and  so  the  current  delivered  by  the  armature  is 
not  only  direct  but  also  steady. 

In  practice,  however,  it  would  be  difficult  to  make  a  good  con- 
tact directly  with  the  wires  of  the  armature,  because  the  wires 
must  be  carefully  insulated  from  each  other  and  from  the  iron 
core ;  and  so  the  various 
turns  of  wire,  or  groups  of 
turns,  have  branch  wires 
which  lead  off  to  the  com- 
mutator segments,  as  in 
figure  376. 

The  commutator  con- 
sists of  copper  bars,  or 
segments,  which  are 

arranged  around  the  shaft       Fig.  376.     Ring  armature  with  commutator. 


ARMATURES 


379 


and  insulated  from  each  other  by  thin  plates  of  mica  (Fig.  377). 
To  get  a  satisfactorily  steady  current  there  should  be  many  seg- 
ments in  a  commutator,  so  that  the  brushes  may  always  be 
connected  to  the  armature  circuit  in  the 
most  favorable  way. 

342.  Drum  armature.    Since  very  little 
flux  passes  across  the   air  space  in  the 
center  of  a  Gramme-ring  armature,  the 
wires  on  the  inner  surface  of  the  ring  do 
not  cut  lines  of  magnetic  force  and  are 
useless,  except  to  connect  the  adjoining 
wires  on  the  outer  surface.     Furthermore, 
it  is  very  inconvenient  to  wind  the  wire 
on  an  armature  of  the  ring  form.     For 
these   reasons  most  armatures  are  now 
of  a  drum  type.     In  this  form  the  core  is 
made  with  slots  along  the  circumference, 
in  which  the  wires  lie  (Fig.  378).     Since 
the  active  wires  in  one  slot  are  connected 
across  the  end  to  active  wires  in  another 
slot,  there  are  no  idle  wires  inside  the  core. 

343.  Multipolar  generators.     The  machines  which  have  been 
described  are  called  bipolar  machines.     For  commercial  pur- 
poses, especially  in  large  machines,  it  is  common  practice  to  use 

four,  six,  eight,  or 
even  more  poles. 
Such  machines  are 
called  multipolar. 
By  increasing  the 
number  of  poles, 
we  can  get  the 
commercial  volt- 
ages (110,  220,  or 
500  volts)  at  much  slower  speeds  than  would  be  necessary  in  a 
bipolar  machine.  We  have  already  seen  that  the  voltage  de- 


Fig.  377.  Commutator  and 
brush  with  its  holder. 


Fig.  378. 


Slotted  armature  core,  drum  type, 
wound. 


Partly 


380 


INDUCED  CURRENTS 


pends  on  the  rate  at  which  the  wires  of  the  armature  cut  the 
lines  of  magnetic  force.  But  in  a  four-pole  machine  (Fig.  379) 
each  wire  on  the  armature  cuts  a  complete  set  of  lines  of  force 
four  times  in  each  revolution  instead  of  twice  as  in  a  two-pole 


Fig-  379-     Four-pole  generator  and  its  diagrammatic  cross  section. 

machine.  For  this  reason  the  speed  of  a  four-pole  machine  is 
one  half  the  speed  required  in  a  two-pole  ma- 
chine for  the  same  voltage.  Furthermore,  the 
multipolar  machine  is  more  economical  to 
build  because  it  requires  less  iron  to  carry 
the  magnetic  flux.  It  will  be  observed  from 
the  diagram  (Fig.  379)  that  every  other  brush 
is  positive  and  is  connected  to  the  positive 
terminal  of  the  machine. 

344.    Excitation  of  the  field  of  generators.     In 

the  magneto  (Fig.  380)  the  magnetic  field  is  sup- 
plied by  permanent  steel  magnets.     In  most  other    Fi«-.3f°-     Magneto 
',  A'     f>  i  i-    o        •  -,     -i-,  with      permanent 

generators  the  magnetic  neld  is  furnished  by  power-        magnets  and  slot- 

ful  electromagnets.     Sometimes  the  current  needed       ted  armature  core. 


EXCITATION  OF   THE  FIELD  OF  GENERATORS     381 


to  excite  these  magnets  is  supplied  by  some  outside  source,  such  as 
a  storage  battery ;  but  generally  the  machine  itself  furnishes  the  ex- 
citing current.  There  are  three  types  of  generators,  differing  in  the 
method  of  exciting  the  field  coils:  (1)  series-wound,  in  which  the 
whole  current  generated  passes 
through  the  field  coils  on  its  way  to 
the  external  circuit ;  (2)  shunt-wound, 
in  which  the  field  is  excited  by  divert- 
ing a  small  part  of  the  main  current, 
the  field  coils  and  the  external  circuit 
being  in  parallel  or  in  shunt ;  and  (3) 

compound-wound,  with  both  series  and 

.,  Fig.  381.     Connections  of  a  series 

shunt  coils.  arc-light  machine. 

In  the  series  generator  (Fig.  381) 

the  field  coils  are  wound  with  a  few  turns  of  large  wire.  When  the 
current  in  the  external  circuit  increases,  the  field  is  more  highly  mag- 
^  netized,  and  so  a  higher  voltage  is 

available  to  supply  the  current. 
This  machine  is  used  to  furnish 
current  for  arc  lamps  which  operate 
on  a  constant  current. 

When  the  field  is  shunt-wound 
(Fig.  382),  the  coils  have  many  turns 
of  small  wire ;  for  in  this  case  it  is 
desirable  to  divert  as  little  current 


Rheostat 


Fig.   382.     Connections  for 
wound  generator. 


shunt- 


as  possible  from  the  main  circuit, 
and  so  the  resistance  of  the  field 
coils  should  be  high.  Such  machines  are  run  at  constant  speed.  When 
more  load  is  thrown  on  the  machine,  that  is,  when  more  lamps  are 
turned  on,  so  that  more  current  is  needed,  the  terminal  voltage  drops 
a  little.  This  decreases 
the  current  in  the  field 
coils  and  still  further  re- 
duces the  terminal  volt- 
age. A  shunt  machine, 
therefore,  cannot  be  used 
when  very  constant  volt- 
age is  desired. 

This  drop  in  the  termi- 
nal voltage  of  shunt  gen- 
erators under  heavy  loads 
can  be  overcome  by  the 


Fig.  383.    Connections  for  compound-wound 
d-c.  generator. 


382 


INDUCED  CURRENTS 


use  of  the  compound-wound  generator  (Fig.  383),  which  is  the  one 
most  commonly  used.  Here  the  voltage  is  kept  constant  by  adding  a 
series  coil  of  a  few  turns ;  this  tends  to  raise  the  voltage  when  the 
current  increases,  just  as  in  a  series  generator.  If  the  coils  are  care- 
fully adjusted,  the  voltage  remains  practically  constant  at  all  loads. 


Fig.  384.     Direct-current  generator  connected  directly  to  a  steam  engine. 

345.  Source  of  energy  in  the  generator.  It  is  important  to 
remember  that  the  electric  generator  cannot  of  itself  make 
electricity,  but  can  only  transform  mechanical  energy  into 
electrical  energy.  For  example,  if  we  want  to  light  a  house  with 
electricity,  it  is  not  enough  for  us  to  buy  a  generator  ;  we  must 
also  get  a  steam  engine  (Fig.  384),  a  gas  engine,  or  a  water 
wheel  with  which  to  drive  the  generator.  We  have  already  seen 
that  the  induced  current  is  always  in  such  a  direction  as  to 
oppose  the  motion  of  the  wire.  Consequently,  the  greater 
the  current  in  the  generator,  the  greater  the  power  needed  to 
turn  it.  Large  generators,  such  as  are  used  in  power  stations 
to  furnish  electricity  for  street  railways  and  city  lighting 


THE   ELECTRIC   MOTOR  383 

systems,  sometimes  require  steam  engines  of  20,000  to  40,000 
horse  power  capacity. 

QUESTIONS 

1.  If  a  person  stands  facing  in  the  direction  of  a  magnetic  flux3 
and  thrusts  downward  a  wire  which  he  holds  in  his  two  hands,  inj 
which  direction  is  the  induced  e.m.f .  ? 

2.  What  are  the  three  factors  which  determine  the  voltage  of  a" 
generator  ?     How  does  each  affect  the  voltage  ? 

3.  How  many   revolutions    per   minute    (r.p.m.)    would   a   single- 
coil  bipolar  dynamo  have  to  make  in  order  that  the  current  might  have ' 
60  cycles  per  second  ? 

4.  How  many  revolutions  per  minute  would  an  eight-pole  generator! 
have  to  make  in  order  to  generate  a  60-cycle  alternating  current  ? 

6.  Why  are  carbon  blocks  generally  used  instead  of  copper  brushes 

ELECTRIC  MOTOR 

346.  The  generator  as  a  motor.    We  have  already  seen  that 
a  generator,  when  driven  by  a  steam  engine,  gas  engine,  or 
water  wheel,  may  generate  electricity.     Now  we  shall  see  how 
this  electric  current  can  be  supplied  to  a  second  machine,  ex- 
actly like  a  generator  but  called  a  motor,  which  may  be  used 
to  drive  an  electric  car,  a  printing  press,  a  sewing  machine,  or 
any  other  machine  requiring  mechanical  energy.     In  short, 
the  generator  is  a  reversible  machine,  and  sometimes  in  shops, 
and  often  on  self-starting  automobiles,  the  same  machine  is 
driven  as  a  generator  part  of  the  time,  and  used  as  a  motor  to 
drive  another  machine  the  rest  of  the  time. 

Structurally,  the  motor,  like  the  generator,  consists  of  an 
electromagnet,  an  armature,  and  a  commutator  with  its  brushes. 
To  understand  how  these  act  in  the  motor,  however,  we  must 
get  a  clear  idea  of  the  behavior  of  a  wire  carrying  an  electric 
current  in  a  magnetic  field. 

347.  Side  push  of  a  magnetic  field  on  a  wire  carrying  a  current. 

We  stretch  a  flexible  conductor  loosely  between  the  two  binding  posts 
A  and  B,  so  that  a  section  of  the  conductor  lies  between  the  poles  of 


384 


INDUCED   CURRENTS 


an  electromagnet,  as  shown  in  figure  385.  Let  the  exciting  current 
be  so  connected  to  the  electromagnet  that  the  poles  are  N  and  S  as 
shown.  Then,  if  a  strong  current  from  a  storage  battery  is  sent  through 
the  conductor  from  A  to  B  by  closing  the  key  K,  it  will  be  seen  that 


Fig.  385.     Side  push  on  wire  carrying  a  current. 

the  wire  between  the  poles  of  the  magnet  is  instantly  thrown  upward, 
If  the  current  is  sent  from  B  to  A,  the  motion  of  the  conductor  is 
reversed,  and  it  is  thrown  downward. 

The  magnetic  field  between  the  poles  of  a  strong  magnet 
is  practically  uniform  and  is  represented  by  parallel  lines  of 
force  shown  in  figure  386. 


N 


Fig.  386.   Uniform  magnetic 
field  of  magnet  alone. 


Fig.  387.    Field 
of  current  alone. 


Fig.  388.  Lines  of  force  about 
a  wire  carrying  current  in  a 
magnetic  field. 


It  will  help  us  to  understand  this  side  push  exerted  on  a  cur- 
rent-carrying wire  in  a  magnetic  field  if  we  recall  that  every 
current  generates  a  magnetic  field  of  its  own,  the  lines  of  which 
are  concentric  circles.  Figure  387  shows  a  wire  carrying  a 
current  in,  that  is,  at  right  angles  to  the  paper  and  away  from 
us.  The  lines  of  force  are  going  around  the  wire  in  clockwise 
direction. 


THE   ACTION  OF  A    MOTOR 


385 


If  we  put  the  wire,  with  its  circular  field,  in  the  uniform  field 
between  the  N  and  S  poles  of  the  magnet,  the  lines  of  force 
are  very  much  more  crowded  above  the  wire  (Fig.  388)  than 
below.  But  we  have  seen  in  section  252  that  we  can  think  of 
magnetic  lines  of  force  as  acting  like  stretched  rubber  bands 
which  would,  in  this  case,  push  the  wire  down.  If  the  current 
in  the  wire  is  reversed,  the  crowding  of  the  lines  of  force  comes 
below  the  wire,  and  it  is  pushed  up. 

348.  Motor  rule  of  three  ringers.     The  rule  for  remembering 
which  way  this  side  push  on  a  wire  in  a  magnetic  field  will  move 
the  wire  is^  precisely  the  same  as  that  for  the  generator,  except 
that  the  left  hand  instead  of  the  right  is  used. 

349.  The  action  of  a  motor.     In  motors,  as  in  generators, 
the  drum  type  of  armature  (see  section  342)  is  almost  exclusively 
used.     It  will    be  remembered  that  in  this  type    the  active 
wires  lie  in  slots  along  the  outside 

of  the  drum,  as  in  figure  389  ;  and 
the  wiring  connections  across  the 
ends  of  the  armature  are  such  that 
when  the  current  is  coming  out 
on  one  side  —  say  the  right  —  it 
will  be  going  in  on  the  other  side  — 
the  left.  Just  how  these  wiring  pig<  3g9> 
connections  are  made  is  not  im- 
portant for  the  present  purpose ;  and  indeed  there  are  many 
different  ways  in  which  they  can  be  arranged.  In  any  case, 
from  what  has  just  been  said,  it  will  be  clear  that  the  wires 
(O)  on  the  right  side  of  the  armature  will  be  pushed  upward, 
and  those  (©)  on  the  left  side  of  the  armature  will  be  pushed 
downward  by  the  magnetic  field.  In  other  words,  there  will 
be  a  torque  tending  to  rotate  the  armature  counter-clock- 
wise. The  amount  of  this  torque  depends  on  the  number  and 
length  of  the  active  wires  on  the  armature,  on  the  current  in 
the  armature,  and  on  the  strength  of  the  magnetic  field. 

Another  way  of  looking  at  this  action  is  to  notice  that  the 


Connections  of  a  drum- 
wound  motor. 


386 


INDUCED  CURRENTS 


effect  of  these  armature  currents  is  such  as  to  make  the  armature 
core  a  magnet,  with  its  north  pole  at  the  bottom  and  its  south 
pole  at  the  top.  The  attractions  and  repulsions  between  these 
poles  and  those  of  the  field  magnet  cause  the  armature  to  rotate 
as  indicated  by  the  arrows. 

The  function  of  the  commutator  and  brushes  is,  as  in  the  gen- 
erator, to  reverse  the  current  in  certain  coils  while  the  armature 
rotates,  in  order  to  keep  the  current  circulating,  as  shown  in 
figure  389. 

360.  Forms  of  motors.  Direct-current  generators  and  motors 
are  often  of  identical  construction.  Thus  we  have  series  motors, 

such  as  are  used  on 
street  cars  and  auto- 
mobiles, and  shunt 
motors,  such  as  are 
used  to  drive  ma- 
chinery in  shops. 
So  also  we  have  bi- 
polar and  multipolar 
motors.  When  it  is 
desirable  that  a 
motor  shall  run  at 
a  slow  speed,  it  is 
built  with  a  large 
number  of  poles. 

Between  the  main 
poles  of  most  mod- 
ern d-c.  generators 
and  motors  are 
smaller  poles,  called 
interpoles  or  corn- 
mutating  poles  (Fig. 
390),  which  are  sup- 
plied with  series  field 
coils  so  that  their  strength  depends  upon  the  armature  current.  They 
are  not  there  to  generate  power  in  the  armature,  but  are  merely  to 
keep  the  brushes  from  sparking  on  heavy  loads  or  high  speeds.  For 
the  explanation  of  their  action,  the  student  is  referred  to  special  books 
on  electrical  machinery. 


Fig.  390.     Direct-current  four-pole  motor  with  four 
interpoles. 


STARTING  A   MOTOR  387 

351.  Back  e.m.f .  in  motor.     Suppose  we  connect  an  incandescent 
lamp  in  series  with  a  small  motor.     If  we  hold  the  armature  stationary, 
and  throw  on  the  current  from  a  service  line  or  storage  battery,  the 
lamp  will  glow  with  full  brilliancy  ;  but  when  the  armature  is  running, 
the  lamp  grows  dim. 

This  shows  that  a  motor  uses  less  current  when  running  than 
when  the  armature  is  held  fast.  The  electromotive  force  of  the 
line  or  battery  and  the  resistance  of  the  circuit  are  not  changed 
by  running  the  motor.  Therefore,  the  current  must  be  dimin- 
ished by  the  development  of  a  back  electromotive  force,  which 
acts  against  the  driving  e.m.f. 

Since  a  motor  has  a  series  of  armature  wires  cutting  mag- 
netic lines  of  force,  it  is  bound  to  generate  an  e.m.f.  in  these 
wires.  That  is,  every  motor  is  at  the  same  time  a  generator. 
The  direction  of  this  induced  e.m.f.  will  always  be  opposite 
to  that  driving  the  current  through  the  motor. 

Just  as  in  the  generator,  when  the  armature  revolves  faster, 
the  back  e.m.f.  is  greater,  and  the  difference  between  the  im- 
pressed e.m.f.  and  the  back  e.m.f.  is  therefore  smaller.  This 
difference  is  what  drives  the  current  through  the  resistance  of 
the  armature.  So  a  motor  will  draw  more  current  when  run- 
ning slowly  than  when  running  fast,  and  much  more  when 
starting  than  when  up  to  speed. 

FOR  EXAMPLE,  suppose  the  impressed,  or  line,  voltage  on  a  motor  is  110 
volts,  and  the  back  e.m.f.  is  105  volts.  Then  the  net  voltage  which  will 
force  current  through  the  armature  is  1 10  —  105,  or  5  volts.  If  the  arma- 
ture resistance  is  0.5  ohms,  the  armature  current  is  5.0/0.5,  or  10  am- 
peres. But  if  the  whole  voltage  (110  volts)  were  thrown  on  the  arma- 
ture while  at  rest,  the  current  would  be  110/0.5,  or  220  amperes. 

352.  Starting  a  motor.     When  a  motor  starts  from  rest, 
there  is,  of  course,  no  back  e.m.f.  at  first,  and  if  the  motor 
is  thrown  directly  on  the  line,  there  will  be  such  an  exces- 
sive current  as  to  "  burn  out  "  the  armature.     To  prevent 
this  first  rush  of  current,  a  starting  resistance  is  put  into  the 


388 


INDUCED   CURRENTS 


circuit  at  first,  and  cut  out  step  by  step  as  the  machine  speeds 
up.     The  device  for  doing  this  is  shown  in  figure  391. 

APPLICATIONS  OF  THE  MOTOR 

353.   Shunt  motors.     The   transmission   of    power   through 
shops  and  factories  by  means  of  shafting,  cables,  and  belts  is 

dangerous,  noisy,  and  uneconom- 
ical. In  a  modern  system,  elec- 
tric power  is  generated  in  a 
central  power  house,  is  transmit- 
ted to  various  parts  of  the  plant, 
and  is  used  in  electric  motors  to 
drive  either  individual  machines 
or  groups  of  machines.  When 
electrical  transmission  is  used, 
the  danger  and  inconvenience  of 
belts  and  shafting  are  avoided, 
the  machines  can  be  set  in  any 
position,  and  their  speed  can  be 
easily  controlled  by  field  rheo- 
stats. In  shops  and  factories  thus 
equipped,  shunt  motors  are  com- 
monly used ;  for  constant  speed  motors  are  required,  and  the 
speed  of  a  shunt  motor  under  no  load,  or  a  light  load,  is  nearly 
the  same  as  at  full  load. 
Electric  motors  have 
also  become  a  great 
convenience  and  com- 
fort in  the  household. 
Thus,  we  have  little 
shunt  motors  to  drive 
sewing  machines  (Fig. 

392)  and  to  drive  Fig'  392  Sewing  machine  run  by  a  shunt  motor, 
the  compressors  of  the  small  refrigerating  plants  for  iceless 
refrigerators. 


Fig.  391-    Diagram  of  starting  box 

connected  with  shunt-wound  motor. 


SERIES  MOTORS 


389 


354.  Series  motors.  On  cranes  and  on  electric  automobiles 
and  cars,  series  motors  are  used,  because  this  type  of  motor  has 
a  large  starting  torque.  The  torque  in  a  series  motor  is  pro- 
portional to  the  square  of  the  current,  while  in  a  shunt  motor 
it  is  directly  proportional  to  the 
current.  The  fact  that  the  torque 
in  a  series  motor  is  largest  when 
the  speed  is  slowest  (because  there 
is  little  back  e.m.f.)  makes  it 
just  the  kind  of  motor  for  crane 
or  vehicle  work.  When  the  load 
on  a  series  motor  drops  to  zero, 
the  motor  may  "  race  "  ;  that  is, 
go  faster  and  faster  until  the 
armature  flies  to  pieces.  For  this 
reason,  series  motors  are  connected, 
either  directly  (on  the  same  shaft) 
or  by  cogwheels,  to  the  machines 
which  are  to  be  driven,  so  that 
they  can  never  escape  their  load. 

Figure  393  shows  a  street-car  motor  with  its  case  lifted  to 
display  the  inside  arrangement.  The  field  consists  of  four  short 
poles  projecting  from  the  case,  which  serves  both  to  protect 
the  motor  and  as  a  path  for  magnetic  flux.  The  armature  re- 
volves so  rapidly  that  its  speed  has  to  be  reduced  by  a  pair  of 
cogwheels,  the  larger  of  which  is  on  the  axle  of  the  driving 
wheels,  and  is  not  shown  in  the  picture.  These  make  the 
speed  of  the  axle  about  one  fourth  that  of  the  motor. 

Street  cars  are  usually  operated  on  a  direct-current  system. 
A  large  multipolar,  compound-wound  generator  at  the  power 
station  maintains  about  550  volts  between  the  trolley  or  third 
rail  and  the  track.  A  "  feeder,"  or  cable  of  low  resistance, 
is  run  parallel  to  the  trolley  wire  and  connected  to  it  at  inter- 
vals, to  avoid  a  large  voltage  drop  in  the  line  when  a  number 
of  cars  are  taking  current  at  a  distance  from  the  power  plant 


Fig.  393- 


Street-car  motor  with  top 
of  case  lifted. 


390 


INDUCED   CURRENTS 


The  current  (Fig.  394)  passes  down  the  trolley  pole  into  the  con- 
troller. This  is  an  ingenious  arrangement  of  switches  by  which 
the  motorman  can  start  his  car  with  both  motors  in  series  and 
with  the  starting  resistance  all  in ;  then  by  moving  a  lever  he 


Feeder 


Trolley 


Trolley 


S.R? 


Armature 


Fig.  394-     Diagram  showing  the  fundamental  features  of  the  electric  railway. 

gradually  cuts  out  the  starting  resistance  and  finally  throws  both 
the  motors  in  parallel,  as  shown  in  figure  395.  Thus,  when  start- 
ing, each  motor  receives  less  than  half  the  line  voltage,  and  when 
running  at  full  power,  gets  full  voltage.  The  current  leaves  the 
motors  by  the  wheels,  and 
goes  back  to  the  power 
station  through  the  rails. 

355.  Efficiency  of  the 
electric  motor.  One  rea- 
son for  the  extensive  use 
of  electric  motors  is  their 
great  efficiency,  sometimes 
as  high  as  80%  or  90%. 
The  efficiency  of  a  motor, 
just  as  of  any  machine, 
means  the  ratio  of  output 
to  input.  We  can  easily 
measure  the  number  of 
amperes  and  the  number 
of  volts  supplied  to  the 
motor  and  thus  compute  the  watts  put  in. 

To  get  the  output  of  mechanical   work,   engineers   usually 
make  a  "  brake  test."     One  simple  form  of  brake  consists  of 


Armature 


Field 


Rail 


Rail 
Series 

Fig.  395.     Diagram  of  series-parallel  control 
of  electric  cars. 


EFFICIENCY  OF   THE  ELECTRIC   MOTOR 


391 


a  belt  or  cord  attached  to  two  spring  balances  and  passing  under 
a  pulley  on  the  motor  shaft,  as  shown  in  figure  396. 

If  the  pulley  rotates  as  indicated,  it  is  evident  that  one  spring 
balance  will  have  to  exert  more  force  than  the  other  because  of 
the  friction  of  the 
pulley  on  the  cord. 
The  amount  of  fric- 
tion is  equal  to  the 
difference  between 
the  readings  of  the 
two  balances,  and  it 
is  exerted  each  min- 
ute through  a  dis- 
tance equal  to  the 
circumference  of  the 
pulley  times  the  rev- 
olutions per  minute. 


The  work  done  in 


Measuring  the  output  of  a  motor  by  means 
of  a  brake. 


Fig.  396. 

one  minute  is  equal 

to  the  friction  times  the  distance  per  minute. 

Finally,  if  we  express  the  output  and  input  in  some  common 
unit  of  power  and  divide,  we  have  the  efficiency.  It  will  be 
helpful  to  know  that 


1  watt 


Fig.  397-     Diagram  of 
a  bipolar  motor. 


44.3  foot  pounds  per  minute, 
6.12  kilogram  meters  per  minute. 

QUESTIONS  AND  PROBLEMS 

1.  Figure  397  represents  a  bipolar  motor 
with  the  armature  revolving  counter-clock- 
wise. Copy  it  and  indicate  by  dots  and  crosses  * 
in  the  circles  the  direction  of  the  various  cur- 
rents in  both  the  armature  and  field  coils. 

*  A  cross  in  a  circle  represents  the  feathers  of  an 
arrow  piercing  the  paper,  and  means  a  current  going 
in.  A  dot  in  a  circle  means  a  current  coming  out. 


392  INDUCED  CURRENTS 

2.  What  is  the  armature  resistance  of  a  motor  in  which  the  arma- 
ture current  is  4  amperes,  the  impressed  e.m.f.  is  115  volts,  and  the 
back  e.m.f.  is  112  volts? 

3.  Find  the  back  e.m.f.  in  a  motor  in  which  the  armature  re- 
sistance is  0.3  ohms,  the  current  is  15  amperes,  and  the  impressed 
voltage  is  110  volts. 

4.  How  much  current  will  be  drawn  by  a  motor  whose  efficiency 
is  90%,  when  it  is  developing  5  horse  power  and  is  connected  to  the 
110- volt  service? 

6.  When  a  certain  motor  was  tested  by  the  brake  test,  it  took  67 
amperes  at  113  volts  and  developed  8.5  horse  power.  Calculate  its 
efficiency. 

6.  What  advantages  are  there  in  driving  the  propellers  of  an 
ocean  liner  by  electric  motors?    What  advantages  in  a  battleship? 

7.  Why  are  electric  cars  not  more  generally  operated  on  storage 
cells  instead  of  by  an  overhead  or  third-rail  system  of  transmission? 

8.  What  methods  are  used  to  make  the  track  of  a  street-car  system 
a  better  conductor  ? 

9.  Does  it  make  any  difference  which  end  of  the  field  coils  of  a 
shunt-wound  generator  is  connected  with  the  positive  brush?     If  you 
have  an  experimental  generator,  try  it. 

10.  The  speed  of  a  shunt-wound  motor  can  be  controlled  by  putting 
an  auxiliary  resistance,  called  a  field-rheostat,  in  series  with  its  field 
coils,  so  as  to  decrease  the  current  through  them.  Will  this  increase 
or  decrease  its  speed?  Why?  If  you  have  an  experimental  motor, 
try  it. 

PRACTICAL  EXERCISE 

Testing  a  starter-generator.  Get  a  secondhand  starter  (such  as  a 
Dodge  or  a  Ford)  from  an  automobile  repair  shop.  Take  it  apart 
and  examine  the  field  coils,  the  armature,  commutator,  and  brushes. 
Reassemble  the  machine  and  measure  its  efficiency  as  a  starting 
motor.  Find  out  how  the  third-brus'h  operates  to  regulate  the  current 
when  charging  the  storage  battery.  (See  Hobbs,  Elliott,  and  Consoliver's 
The  Gasoline  Automobile  —  McGraw-Hill  Book  Co.) 

OTHER  APPLICATIONS  OF  INDUCED  CURRENTS 

356.  Currents  induced  by  currents.  Since  an  electro- 
magnet can  be  made  more  powerful  than  a  steel  magnet,  we 


INDUCTION   COIL 


393 


Fig-  398.     A  moving  electromagnet 
generates  a  current. 


should  expect   greater  induced   currents   when   we   move   an 
electromagnet  near  a  coil. 

We  shall  connect  the  secondary  coil  S  in  figure  398  to  a  galvanometerr 

and  the  primary  coil  P  to  a  battery.     When  we  move  the  current- 
carrying  primary  coil  P  either  into  or 

out  of  the  other  coil  S,  a  current  is 

induced,   just   as  when  we  move  a 

magnet  in  and  out  of  a  coil.     The 

induced  current  is,   however,   much 

greater.     We  find  also  that  a  stronger 

current  in  the  coil   P  increases  the 

strength  of  the  magnetic  field,  and 

so  of  the  induced  current. 

We  may  also  increase  the  induced 

current  by  inserting  an  iron  core  in- 
side the  primary  coil.     This  greatly 

strengthens  the  magnetic  field  and  so 

increases  the  number  of  lines  of  force 

about  the  coil. 

If  we  put  the  primary  coil  with  its  iron  core  inside  the  secondary 

coil,  we  can  generate  an  induced  current  by  opening  and  closing  a 

switch  in  the  primary  circuit. 
When  the  switch  is  opened  and 
closed,  the  deflections  are  in 
opposite  directions. 

In  general  we  see  that  an 
induced  current  is  set  up  in 
a  coil  whenever  there  is  a 
change  in  the  number  of  lines 
of  magnetic  force  passing 
through  the  coil. 

357.  Induction  coil.  In 
the  induction  coil  (Fig.  399) 
the  core  /  is  made  of  soft- 
iron  wires ;  the  primary  coil 
P  consists  of  a  few  turns  of 
large  copper  wire,  and  the 
secondary  coil  S,  which  is 


Fig.  399- 


Induction  coil  and  diagram  of 
connections. 


394 


INDUCED  CURRENTS 


carefully  insulated  from  the  primary,  contains  many  turns 
of  very  small  silk-covered  copper  wire.  To  make  and  break 
the  primary  current  very  rapidly,  an  interrupter  H  is  com- 
monly made  to  operate  on  the  end  of  the  coil.  This  auto- 
matic make-and-break  works  exactly  like  the  vibrating  electric 
bell  described  in  section  301.  When  the  primary  circuit  in 
such  a  coil  is  broken,  the  current  tends  to  keep  on  as  if  it  had 
inertia,  and  may  jump  the  switch  gap  at  A  even  after  it  has 
opened  slightly.  This  slows  up  the  "  break  "  and  weakens  the 
induced  e.m.f .  So  a  condenser  C  is  connected  across  the  gap. 
It  is  usually  made  of  sheets  of  tin  foil,  insulated  by  paraffin  paper, 
arranged  as  shown  in  figure  399.  This  furnishes  a  storage  place 
into  which  the  current  can  surge  when  broken,  and  diminishes 
the  sparking  at  the  interrupter.  Even  with  a  condenser  there 
is  some  sparking,  and  so  the  contact  points  have  to  be  tipped 
with  silver  or  tungsten  and  frequently  cleaned. 

Coils  are  generally  rated  according  to  the  distance  between 
the  terminals  of  the  secondary  across  which  a 
spark  will  jump.  When  the  coil  is  in  opera- 
tion, sparks  jump  across  this  gap  in  rapid 
succession,  provided  the  terminals  are  close 
enough  together.  This  type  of  coil  is  some- 
times called  a  Ruhmkorff  coil. 

358.  Uses  of  induction  coils.  The  most 
important  practical  application  of  the  induc- 
tion coil  is  undoubtedly  for  ignition  in  gas 
engines.  To  make  a  spark  jump  between 
the  terminals  of  the  spark  plug  (Fig.  400), 
several  thousand  volts  are  required. 


1  H«-  Porcelain 


Spark  Gap 


Fig.  400.  Cross 
section  of  a  gas- 
engine  spark 
plug. 

There  are  a  number  of  systems  for   producing 

this  high- voltage  current  on  automobiles.  In  the  Ford  car  a  mag- 
neto with  rotating  horseshoe  magnets  induces  an  alternating  current 
in  a  series  of  coils  which  are  attached  to  the  flywheel  case.  Then  this 
low-tension  current  is  raised  to  a  high  voltage  by  four  induction  coils 
and  applied  directly  to  the  spark  plugs.  In  the  wiring  diagram  shown 


SELF-INDUCTION 


395 


in  figure  401,  it  will  be  seen  that  the  primary  circuit  includes  a  timer, 
which  is  a  rotating  switch  for  closing  the  circuit  for  each  of  the  four 
cylinders  at  just  the  right  time.  It  will  also  be  seen  that  the  return 
high-voltage  circuit  is  through  the  motor  frame  itself. 

On  the  Liberty  aircraft  engine  and  on  many  automobile  and  marine 
engines,  the  direct  current  is  supplied  by  a  generator  and  a  storage 


Timer 


Spark  Plug 


Return  CurrentJL.T.) 
(Grounded'fliru  Motor) 


Cyl.  No.  4 


Magneto  Coil  Assembly 


Iron  Core'' 


Low  Voltage  Current 

High  Voltage  Current 

Grounded  Current 

Fig,  401.     Diagram  of  the  ignition  system  of  the  Ford  automobile  engine. 
A  coil  for  each  cylinder. 

battery  with  a  voltage-regulating  device.  The  low-voltage  current 
is  transformed  to  a  high-voltage  current  by  means  of  an  induction  coil. 
In  this  system  there  are  one  induction  coil,  one  interrupter,  and  a  dis- 
tributor which  transmits  the  high-voltage  current  to  the  various  spark 
plugs  in  turn.  The  principle  of  this  system  is  shown  in  figure  402. 

In  still  another  system  a  high-tension  magneto  is  used,  which  com- 
prises within  itself  the  means  for  generating  and  intensifying  the 
current,  so  that  all  that  is  needed  to  complete  the  ignition  system 
is  a  set  of  spark  plugs  and  some  connecting  wires. 

Induction  coils  are  also  used  in  connection  with  storage  bat- 
teries in  portable  apparatus  for  exciting  X-ray  tubes  and 
for  setting  up  electric  waves  for  radio  telegraphy.  These  will 
be  described  in  Chapter  XXIII. 

359.  Self-induction  or  inductance.  If  a  coil  of  wire  with 
many  turns  and  with  a  soft-iron  core  is  connected  with  a  bat- 


396 


INDUCED  CURRENTS 


tery  (Fig.  403),  it  can  be  shown  that  when  the  switch  is  closed 
the  current  does  not  instantly  attain  its  full  value  as  determined 
by  Ohm's  law.  The  reason  for  this  growth  of  the  current 


Ground 


Fig.  402.     Diagram  of  automobile  ignition  system  using  battery,   spark  coil,  and 
high-tension  distributor. 

(which  of  course  takes  a  very  short  time)  is  the  fact  that  the 
current  is   building   up  a  magnetic   field,    and   that    as   this 


Time 


k  Closed 

Fig.  403.     Growth  and  decay  of  current  in  an  inductive  circuit. 

field  grows,  its  lines  of  force  cut  the  turns  of  the  coil  and  induce 
in  them  a  voltage,  which  opposes  the  growth  of  the  current. 


APPLICATIONS  OF  SELF-INDUCTION 


397 


When  the  switch  is  opened,  the  original  current  does  not  drop 
instantly  to  zero,  but  tends  to  arc  across  the  switch  gap  and 
keep  on  flowing.  As  the  current's  own  magnetic  field  dies  away, 
the  lines  of  force  again  cut  the  turns  of  the  coil ;  but  this  time, 
in  such  a  direction  that  the  self-induced  voltage  upholds  the  current. 

That  property  of  an  electric  circuit  whereby  it  opposes  a  change 
in  the  current  flowing  is  called  the  self-induction  or  the  inductance 
of  the  circuit.  This  property  of  an  electric  circuit  is  sometimes 
called  its  electromagnetic  inertia,  because  it  is  quite  like  the 
property  of  inertia,  which  we  find  in  all  machines. 

360.  Applications  of  self-induction.  The  principle  of  self- 
induction  is  made  use  of  in  make-and-break  ignition.  A  single 
coil  is  used,  consisting  of  many  turns 
of  wire  wound  on  a  soft-iron  core. 
When  such  a  coil  is  employed  to 
furnish  a  spark  in  the  cylinder  of  a 
gas  engine,  the  circuit  is  as  shown  in 
figure  404.  The  terminals  are  two 
points  inside  the  cylinder  of  the 
engine,  one  stationary  (A)  and  the 
other  moving  (S).  When  A  and  S 
separate,  the  self-induction  of  the  coil  causes  enough  induced 
e.m.f .  to  make  a  spark  jump  across  the  gap  between  them. 

This  is  the  kind  of  coil  which  is  used  to  light  gas  burners 
in  houses  by  means  of  a  battery  current.  If  the  circuit  of  a 
large  electromagnet,  such  as  the  field  of  a  dynamo,  is  broken 
while  one  is  touching  the  conductors  on  either  side  of  the  gap,  the 
current  due  to  self-induction  sometimes  gives  a  severe  shock. 

PRACTICAL  EXERCISE 

Connecting  an  automobile  ignition  system.  Get  the  essential  parts 
of  the  Ford  ignition  system,  such  as  the  spark  plugs,  the  timer,  and  the 
spark  coils.  Connect  them  as  in  figure  401  and  mount  the  spark 
plugs  so  as  to  show  the  successive  sparks  as  the  timer  rotates.  Dry 
cells  may  be  used  in  place  of  the  magneto. 


Fig.  404.  Make-and-break 
spark  coil  used  for  gas- 
engine  ignition. 


398 


INDUCED   CURRENTS 


THE  TELEPHONE 

361.  Telephone  receiver.     In  1876  Alexander  Graham  Bell 
astonished  the  world  by  showing  that  the  sound  of  a  human 
voice  could  be  transmitted  by  electricity.     The  essential  part 
of  his  apparatus  was  what  we  still  use  and  know  as  the  Bell 

receiver.  The  hard-rubber  case 
contains  a  steel  U-shaped  magnet, 
which  has  around  each  pole  a 
coil  of  many  turns  of  very  fine 
wire  (Fig.  405).  A  disk  of  thin 
sheet  iron  is  so  supported  that  its 

Fig.  405.  Parts  of  a  bipolar  tele-  center  does  not  quite  touch  the 

ends  of  the  magnet.  A  hard-rubber 

cap  or  earpiece  with  a  hole  in  the  center  holds  the  disk  in  place. 

To  show  the  operation  of  the  telephone  receiver,  we  may  connect 
a  large  receiver,  in  series  with  a  lamp,  to  the  a-c.  mains  or  to  a  magneto 
which  furnishes  an  alternating  current.  We  immediately  hear  a  loud 
hum.  If  we  hold  the  receiver  upright  and  stand  a  pencil  on  the  dia- 
phragm, it  dances  up  and  down.  The  alternating  current,  sent  through 
the  coil,  alternately  strengthens  and  opposes  the  magnet,  which  attracts 
the  disk  alternately  more  and  then  less,  thus  causing  it  to  vibrate.  This 
sets  the  air  to  vibrating  and  produces  sound. 

362.  The  microphone.     To  show  how  the  right  sort  of  cur- 
rents can  be  produced  to  make  a  telephone  receiver  speak  words 
instead  of  merely  humming, 

we  shall  set  up  an  old- 
fashioned  instrument  called 
a  microphone. 

A  simple  microphone  can  be 
made  out  of  three  lead  pencils,       Fig  4o6     Simple  form  of  microphone, 
or  three  pieces  of  electric-light 

carbon  (Fig.  406).  If  such  a  microphone  is  connected  in  series  with  a 
battery  and  telephone  receiver,  and  a  watch  is  laid  on  its  baseboard, 
the  ticks  can  be  heard  in  the  telephone  even  if  it  is  some  distance  away. 
The  little  jars  which  the  watch  gives  the  baseboard  shake  the  car- 


THE   TELEPHONE  399 

bons  so  that  the  resistance  at  their  points  of  contact  varies  and  thus 
changes  the  current.  The  changing  current  then  pulls  the  telephone 
diaphragm  back  and  forth,  and  sets  the  surrounding  air  in  motion. 

363.  The    telephone   transmitter.     The    modern    telephone 
transmitter   is   simply   a   carefully   designed   microphone.     It 
contains  a  little  box  C  (Fig.  407)  which  is 

filled  with  granules  of  hard  carbon.  The 
front  and  the  back  of  the  box  are  polished 
plates  of  carbon,  and  the  sides  of  the  box 
are  insulators.  The  front  carbon  is  attached 
to  the  center  of  the  diaphragm  D,  and  moves 
in  and  out  a  little  when  the  diaphragm 
vibrates.  The  other  plate  is  fastened  rigidly 
to  the  solid  back  of  the  case.  A  current  Fig.  407.  Carbon  trans- 
from  a  battery  flows  to  the  front  plate,  then  mitter  (cross  section.) 
back  through  the  granules  to  the  other  plate,  and  out  along  the 
telephone  line  to  a  receiver.  When  the  diaphragm  moves  back 
a  little,  it  compresses  the  granules,  their  resistance  decreases,  and 
the  current  gets  stronger  and  pulls  the  diaphragm  of  the  receiver 
back  also.  When  the  transmitter  diaphragm  moves  out,  the 
current  decreases  and  the  receiver  diaphragm  moves  out  also. 
So  all  the  motions  of  the  transmitter  diaphragm  are  reproduced 
by  the  receiver  diaphragm.  If  one  speaks  into  the  transmitter, 
causing  its  diaphragm  to  move  in  a  corresponding  way,  the 
receiver  diaphragm  moves  in  the  same  way  and  produces  the 
same  kind  of  waves  in  the  surrounding  air. 

364.  Central   batteries  and  local  batteries.    The    system 
we  have  just  described  is  the  one  in  use  in  all  large  cities.     The 
battery  is  a  large  storage  battery  (or  a  generator)  at  the  central 
station,  and  is  used  on  all  the  lines  that  happen  to  be  busy  at 
any  instant. 

'  In  many  country  exchanges  and  on  isolated  lines  another 
system,  called  the  local-battery  system,  is  used  because  it  is 
cheaper  to  install  and  maintain.  Even  in  cities  something 
equivalent  to  this  system  is  used  on  long-distance  lines. 


400 


INDUCED  CURRENTS 


line 


""TlTir-         -  Receiver 

Fig.  408.    Diagram  of  local-battery  telephone 

system. 


In  this  system  (Fig.  408)  each  subscriber's  telephone  set  con- 
tains a  few  dry  cells  which  are  connected  in  series  with  his  trans- 
mitter, as  already  described.  But  the  varying  current  pro- 
duced, instead  of  being  sent  directly  out  on  the  line,  goes  to  the 

primary  of  a  little  induc- 
tion coil  and  back  to  the 
battery.  The  secondary 
of  the  induction  coil 
meanwhile  sends  out  into 
the  line  an  induced  cur- 
rent that  varies  exactly 
like  the  primary  current, 
but  is  at  much  higher  voltage.  This  makes  the  "  line  losses  " 
much  smaller,  and  so  more  energy  gets  through  to  the  receiver 
than  if  the  original  current  had  been  transmitted  directly. 
This  system  is  really  better,  electrically,  than  the  central- 
battery  system.  It  is  not  used  in  large  cities,  chiefly  because 
of  the  trouble  involved  in  keeping  so  many  local  batteries  in 
proper  working  condition. 

PRACTICAL  EXERCISE 

Setting  up  a  two-party  telephone  line.  For  full  directions  and 
diagrams,  see  Good's  Laboratory  Projects  in  Physics  (Macmillan  Co.). 

SUMMARY  OF  PRINCIPLES  IN  CHAPTER  XVII 

Induced  current  exists  only  when  the  number  of  lines  of  force 

through  the  circuit  is  changing. 
Induced  current  has  such  a  direction  as  to  oppose  the  motion 

which  causes  it.     Lenz's  law. 

When  a  wire  cuts  lines  of  force,  an  induced  e.m.f.  js  set  up. 
To  get  direction  of  induced  current,  use  right  hand. 
Thumb  shows  the  motion. 
Forefinger  shows  the  flux. 
Center  finger  shows  direction  of  current. 
Magnitude  of  e.m.f.  varies  as  speed  X  flux  X  turns. 


SUMMARY  401 

Commercial  generator  with 

slip  rings  gives  alternating  current, 

commutator  gives  direct  current. 
Generator   does  not    make  energy ;    it   transforms  mechanical 

into  electrical  energy. 
Motor  transforms  electrical  energy  into  mechanical  energy. 

A  wire  carrying  a  current,  when  set  at  right  angles  to  a  magnetic 

field,  is  pushed  sidewise  by  the  field. 
To  get  direction  of  motion,  use  left  hand. 

Every  motor,  when  running,  is  acting  at  the  same  time  as  a 
generator.  The  e.m.f.  of  this  generator  action  opposes  the 
current  driving  the  motor,  and  is  the  back  e.m.f. 

Net  e.m.f.,  which  drives  current  through  armature,  equals 
impressed  e.m.f.  minus  back  e.m.f. 

Ohm's  law  applies  to  a  motor  armature  only  if  net  e.m.f.  is 
used. 

Self-induction,  or  inductance,  means  that  the  magnetic  field 
around  a  coil  tends  to  oppose  any  change  in  the  current. 

QUESTIONS 

1.  How  should  a  coil  of  wire  be  rotated  in  the  earth's  magnetic 
field  to  get  the  maximum  induced  current  ? 

2.  How  might  a  coil  of  wire  be  rotated  in  the  earth's  magnetic 
field  so  as  to  get  no  induced  current  ? 

3.  Why  are  one-coil  armatures  not  used  commercially? 

4.  Why  must  the  power  applied  to  a  generator  armature  be  in- 
creased if  the  current  generated  is  increased  and  the  voltage  is  kept 
constant  ? 

6.   What  becomes  of  the  energy  lost  in  a  generator? 

6.  Why  is  the  price  of  electricity  dependent  on  the  price  of  coal 
or  the  availability  of  water  power? 

7.  Of  what  use  is  residual  magnetism  when  a  generator  is  started  ? 

8.  A   belt-driven,   shunt-wound    generator    is    used    to    charge    a 
storage  battery.     The  belt  breaks,  but  the  machine  keeps  on  running. 
Explain. 


402  INDUCED   CURRENTS 

9.   Why  does  an  electric  truck  take  more  current   going    uphill 
than  on  the  level  ? 

10.  Explain  how  the  law    of    conservation  of   energy    applies    to 
the  input  and  output  of  a  motor. 

11.  What  is  the  difference  in  the  construction  and  use  of  a  field 
rheostat  and  a  starting  rheostat  ? 

12.  Find  out  how  the  motor-generator  used  for  starting  an  auto- 
mobile and  for  charging  a  storage  battery  maintains  a  constant  voltage 
at  varying  speeds. 

13.  What  are  the  advantages  of   the  two-unit   system   (that  is, 
separate  motor  and  generator)  for  starting  an  automobile  and  charg- 
ing its  storage  battery  ? 

14.  What  are  the  essential  differences  between  the  current  in  the 
primary  winding  of  the  induction  coil  and  that  in  the  secondary  wind- 
ing? 

15.  What  is  the  function  of  the  magneto  in  a  local-battery  tele- 
phone system? 

16.  Why  is  it  dangerous  to  touch  the  terminals  of  the  secondary 
of  a  large  induction  coil? 

17.  Why  is  the  induced  e.m.f.  in  the  secondary  of  an  induction 
•coil  so  much  greater  at  the  break  of  the  primary  than  at  the  make? 

18.  Why  is  it  that  the  self-induction  of  a  circuit  is  not  apparent  as 
long  as  the  current  is  steady? 

19.  An  electrical  impulse  passes  over  the  telephone  wires  from 
Boston  to  San  Francisco  in  about  one  fifteenth  of  a  second.    How  long 
would  it  take  sound  to  travel  that  distance  through  the  air? 

20.  In  the  very  first  telephones,  two  telephone  receivers  were  con- 
nected together.     Could  you  use  telephone  transmitters  in  the  same 
way?     Explain. 

PRACTICAL  EXERCISE 

Thermoelectric  currents.  Twist  together  the  ends  of  a  small  copper  wire 
and  a  small  iron  wire  and  connect  the  other  ends  to  a  millivoltmeter. 
Apply  the  heat  of  a  burning  match  to  the  twisted  ends  of  the  wires.  The 
voltmeter  shows  that  an  electric  current  is  generated.  When  the  twisted 
wires  are  cooled  with  ice,  the  current  is  in  the  opposite  direction. 

Find  out  how  a  thermoelectric  pyrometer  is  made  and  how  it  is  used  in 
measuring  the  temperature  of  furnaces. 


CHAPTER   XVIII 
ALTERNATING   CURRENTS 

Why  alternating  currents  are  used  —  the  transformer  — 
long-distance  transmission  —  eddy  currents  —  impedance  — 
a-c.  power  —  capacity  —  alternators  —  polyphase  circuits  — 
a-c.  motors  —  rotating  field  —  squirrel-cage  rotor  —  watt- 
hour  meters  —  rectifiers. 

365.  Why  alternating  currents  are  used.     For  heating  and 
lighting  purposes  an  alternating  current  is  just  as  satisfactory 
as  a  direct  current.     For  plating  and  refining,  an  alternating 
current  cannot  be  used,   because  a  unidirectional  current  is 
necessary  to  make  a  metal  deposit.     If  motors  are  to  be  run 
by  an  alternating  current,  a  special  type  of  motor  is  generally 
used,  which  is  very  different  from  the  ordinary  direct-current 
motor.     The  real  advantage  in  the  use  of  alternating  currents 
is  economy  of  transmission.     This  is  made  possible  by  a  simple 
and  efficient  machine  known  as  a  transformer. 

366.  What  a  transformer  does.     It  must  be  kept  in  mind 
that  a  transformer  is  primarily  a  voltage  changer  and  that  it 
does  not  change  alternating  to  direct   current.    Perhaps  we 
can  best  show  what  a  transformer  does  by  describing  a  bell- 
ringing  transformer,  which  enables  us  to  take  power  from  the 
ordinary  a-c.  lighting  circuit  and  to  use  it  for  operating  bells, 
buzzers,  door  openers,  and  the  like.     This  little  device  changes 
the  110  volts  of  a  lighting  circuit  down  to  the  5,  10,  or  15  volts 
which  are  needed  for  ringing  bells. 

Figure  409  shows  the  exterior  and  interior  construction  of  one  type 
of  bell-ringing  transformer.  The  terminals  A  and  B  are  connected 
through  fuses  to  the  110- volt  a-c.  circuit  and  are  called  the  primary 
terminals.  The  terminals  x  and  y  are  the  secondary  terminals  and 

403 


404 


ALTERNATING  CURRENTS 


A-C.Line 


will  give  10  volts  when  the  primary  voltage  is  110  volts.     When  we 
examine  the  interior  construction,  we  are  surprised  to  find  it  so  simple 

—  merely  an  iron  core  and  two  coils 
of  wire.  The  core  C  consists  of  thin 
sheets  of  annealed  steel  stamped  out 
in  the  proper  shape  to  give  a  closed 
magnetic  circuit.  The  primary  coil 
P  of  enamel-covered  wire  has  about 
880  turns,  and  the  secondary  coil  S 
has  approximately  80  turns. 

367.  The  principle  of  the 
transformer.  In  any  trans- 
former there  are  two  coils  side 
by  side  on  a  common  iron  core. 
When  an  alternating  current  is 
set  up  in  one  coil,  called  the  primary,  it  magnetizes  the  iron 
core,  causing  surges  of  magnetic  flux  first  in  one  direction  and 
then  in  the  opposite  direction.  Since  this  magnetic  flux  passes 
through  the  second  coil,  called  the  secondary,  as  well  as  the 
first,  it  induces  an  alternating  current  in  the  secondary.  Since 
the  same  number  of  lines  of  force  pass  through  both  coils,  the 
volts  per  turn  are  the  same.  Therefore,  the  total  voltage  in  the 
primary  coil  is  to  the  total  voltage  in  the  secondary  coil  as  the 
number  of  turns  in  the  primary  is  to  the  number  of  turns  in 
the  secondary.  This  may  be  expressed  in  the  following  equation  : 


\t--W  volts- 


g.  409.  Bell-ringing  transformer  with 
diagram  of  interior  construction. 


Voltage  on  primary 
Voltage  on  secondary 


turns  of  primary 
turns  of  secondary 


Thus  we  see  that  the  alternating-current  power  is  transferred 
from  the  primary  to  the  secondary  by  means  of  the  magnetic 
flux  in  the  iron  core. 

368.  Ordinary  distributing  transformer.  Since  the  voltage 
of  the  transmission  lines  in  the  street  is  usually  about  2300  volts, 
it  is  necessary  to  transform  it,  or  "  step  it  down,"  to  115  volts 
in  order  to  use  it  safely  in  private  houses.  In  such  a  trans- 
former the  high-tension  coil,  consisting  of  many  turns  of  small 


TRANSFORMERS 


405 


wire,  would  be  connected  to  the  2300-volt  circuit,  and  the  low- 
tension  coil,  consisting  of  a  few  turns  of  large  wire,  would  be 
connected  with  the  lamp  circuit  of  the  houA^Mn  this  case 
the  high-tension,  or  primary,  coil  must  navel  Knes  as  many 
turns  as  the  low-tension,  or  secondary.  ^JWne  secondary 
coil  must  be  made  of  larger  wire  than  the  primary  coil,  because 
the  secondary  current  is  about  twenty  times  the  current  taken 
by  the  primary.  Thus  the  transformer  delivers  the  same 
amount  of  energy  which  it  receives,  except  for  a  small  amount 
(from  2  to  5  per  cent)  which  is  lost  as  heat  in  the  transformer. 
The  efficiency  of  a  transformer  is  therefore  very  high — from  95 
to  98  per  cent. 

Transformers  are  built  in   two  general   types:    (a)    the  core  type 
(Fig.  401,  A),  in  which  the  coils  are  wound  around  two  sides  of  a  rectan- 

,Core 


o 

Fig.  410.     Three  types  of  transformer  ;     A,  core  type  ;  B,  shell  type  ;  C,  H-type. 


gular  iron  core,  and  (6)  the  shell  type  (Fig.  410,  5),  in  which  the  iron 
core  is  built  around  the  laminated  coils.  In  both  these  types  the  cores 
are  built  up  of  thin  sheets  of  annealed  silicon  steel. 

The  most  modern  type  is  really  a  modification  of  the  core  type,  with 
which  are  combined  many  of  the  advantages  of  the  shell  type.  It 
has  the  windings,  or  coils,  on  one  leg  of  the  core,  while  the  other  leg 
is  divided  into  four  parts,  symmetrically  placed  around  the  center  leg, 
on  which  the  coils  are  placed,  as  shown  in  figure  410,  C.  To  keep  the 
coils  insulated,  the  transformer  is  put  into  an  iron  case  and  surrounded 
with  oil.  These  iron  cases  (Fig.  322)  are  commonly  attached  to  poles 
near  houses  wherever  alternating  current  is  used  for  lighting  purposes. 

369.   Uses  of  transformers.     In  electric-light  stations  it  is 
common  practice  to  use  alternators  to  generate  electricity  at 


406 


ALTERNATING  CURRENTS 


2300  volts.  The  current  is  transmitted  at  this  high  voltage 
to  the  various  districts,  where  it  is  transformed,  or  "  stepped 
down,"  to  U^^olts  for  use  in  lighting  houses.  Another  im- 
portant use  j  «>down  transformers  is  to  furnish  large  currents 
at  very  low  iJPpp  for  electric  furnaces  and  electric  welding. 

To  illustrate  this,  we  may  wind  a  turn  or  two  of  very  large  copper 
wire  around  the  core  of  a  small  step-down  transformer  (Fig.  411) 
and  connect  its  primary  to  a  110-volt  a-c.  circuit  (if  one  is  available). 

The  ends  of  the  large  wire  should 
be  attached  to  a  pair  of  iron  nails. 
If,  when  the  current  is  on,  the  tips 
of  the  nails  are  brought  together, 
they  get  red  hot  and  can  be  welded. 

The  adjoining  rails  of  a  car 
track  are  often  welded  together 
in  this  way.  A  heavy  current  is 

Fig.   411.     Experimental    step-down  required  for  a  short  time,  and 
transformer  used  for  welding.  ig    obtained    by    using    a    step_ 

down  transformer,  in  which  the  secondary  consists  of  only  one 
or  two  turns,  made  of  very  large  copper  bars.  The  ends  of  this 
secondary  are  clamped  to  the  rails  which  are  to  be  welded,  one 
on  each  side  of  the  junction.  .-, 

370.  Long-distance  transmission  of  power.  By  the  use  of 
alternating  currents  of  high  voltage,  even  up  to  220,000  volts, 
power  is  now  transmitted  very  long  distances.  For  example, 
electric  power  is  generated  in  hydroelectric  power  plants  in 
the  Sierra  Nevada  Mountains  of  California,  and  transmitted 
about  250  miles  to  Los  Angeles.  To  understand  why  the  eco- 
nomical transmission  of  electricity  demands  such  high  voltage, 
we  should  remember  that  the  power  transmitted  depends  on  the 
product  of  voltage  and  current  strength.  Evidently,  then,  if 
we  can  make  the  voltage  high,  the  current  can  be  low.  But 
a  smaller  current  means  smaller  losses  in  transmission  ;  for  they 
are  due  to  the  heating  effect  of  the  electric  current,  and  we 
have  already  seen  that  this  varies  as  the  square  of  the  current. 


LONG-DISTANCE   TRANSMISSION  OF  POWER      407 


It  is  not  an  unusual  thing  to  see  three  or  six  copper  cables, 
each  about  f  of  an  inch  in  diameter,  suspended  about  75  feet 
above  the  ground  on  steel  towers  (Fig.  412)  and  to  learn  that 
those  wires  are  carrying  40,000  kilowatts  of  ejfcctrical  energy 
Hydroelectric  power  plants 
are  being  developed  all  over 
the  country.  For  example, 
at  Niagara,  power  plants  are 
generating  electricity,  raising 
the  voltage  to  60,000,  and 
transmitting  some  of  the 
enormous  energy  available 
at  the  Falls  to  distant  cities 
like  Buffalo,  Rochester,  and 
Syracuse.  Just  outside  the 
city  limits  there  are  sub- 
stations where  the  voltage 
is  reduced  to  about  2000,  and 
then  it  is  distributed  to  fac- 
tories and  for  general  use  in 
lighting  and  traction.  Before 
the  current  actually  enters' 
the  buildings,  the  voltage  is 
again  stepped  down  to  220 
or  110  volts. 

At  the  power  stations  are 
step-up  transformers,  which 
receive  electric  power  at  from  2300  to  11,000  volts  and  step  it  up 
to  from  50,000  to  220,000  volts  for  the  transmission  lines.  In 
this  process  no  power  is  gained  in  the  transformer,  since  electric 
power  depends  on  the  product  of  voltage  and  current.  We  may 
multiply  the  voltage  perhaps  10  times,  but  at  the  same  time  we 
divide  the  current  by  a  little  more  than  ten,  so  that  we  always 
lose  some  power.  In  very  large  transformers  the  insulating 
oil  has  to  be  water-cooled ;  and  for  high- voltage  installations, 


Fig.  412.     High-voltage  long-distance 
transmission  lines. 


408 


ALTERNATING  CURRENTS 


the  out-of-doors  type  of  transformer  and  switch  (Fig.  413)  is 
largely  superseding  the  indoor  type. 


Fig.  413.     Out-of-doors  transformers  in  which  the  oil  is  water-cooled. 

371.  Eddy  currents.  We  have  seen  that  the  cores  of  transformers 
are  made  of  soft-iron  or  mild-steel  sheets  stamped  out  in  the  de- 
sired shape  and  then  assembled.  In  the  construction  of  induction 
coils,  the  cores  are  made  of  soft-iron  wires,  which  are  put  together  in  a 
bundle.  If  we  examine  the  armature  of  a  dynamo,  we  find  that  the 
iron  drum  is  made  of  laminae  (sheets)  of  mild  steel  which  are  stamped 
out  in  the  shape  of  disks  with  notches  around  the  edge  (Fig.  414), 
and  then  assembled  on  a  framework  called  the  "  spider,"  and  mounted 
on  the  shaft.  In  all  these  cases  the  sheets  or  wires  are  insulated  from 
each  other  by  a  coating  of  shellac,  which  eliminates  what  are  sometimes 
called  Foucault,  or  eddy,  currents. 

We  have  already  seen,  in  studying  the  generator,  that  when  any 
conductor  cuts  lines  of  force,  an  induced  electromotive  force  tends  to 
send  a  current  along  the  conductor.  In  the  generator  copper  wires  are 
provided  to  carry  this  current ;  but  these  wires  are  wound  on  an 


EDDY    CURRENTS 


409 


iron  core,  and  if  this  core  is  itself  an  electrical  conductor,  an  induced 
e.m.f.  will  be  set  up  in  it  as  it  revolves  in  the  magnetic  field.  This 
induced  e.m.f.  would  send 
through 
of  the 


Wooden    Wedge 


Ventilating 


414. 


Laminated  core 
armature. 


of  a  generator 


electric   currents 

certain    portions 

core.   These  so-called  eddy 

currents  would  soon  heat 

the  core,  and  would  also 

retard   the  motion  of  the 

armature  and  waste  power. 

To  reduce  these  currents 

to  as  small  a  value  as  pos- 
sible, the  core  is  laminated 

in  such  a  way  that  the  in- 
sulation  is   transverse   to 

the  direction  in  which  the 

eddy  currents  tend  to  flow. 

372.    Use  of  eddy  currents  in  damping.     To  show  that  eddy  currents 

tend  to  retard  the  motion  of  a  conductor  in  a  magnetic  field,  we  may 
set  up  between  the  poles  of  a  strong  electro- 
magnet a  pendulum  made  of  thick  sheet  copper 
(Fig.  415).  If  the  magnet  is  not  excited,  the 
pendulum  swings  back  and  forth  as  any  pendu- 
lum does ;  but  when  we  throw  on  the  current 
in  the  magnet,  the  copper  pendulum  cannot 
swing  through  the  magnetic  field,  and  is  in- 
stantly checked.  The  eddy  currents  set  up  in 
the  copper  tend  to  retard  the  motion  of  the 
pendulum,  much  as  if  it  were  swinging  in  thick 
sirup. 

This  effect  is  very  useful  in  stopping  the 
vibrations  of  the  moving  coil  of  a  d' Arson vaj 
galvanometer  (section  303).  The  wire  is  usually 
wound  on  a  light  copper  or  aluminum  frame, 
and  the  eddy  currents  in  this  metal  frame  check 

its  swinging.    Such  a  galvanometer  is  called  "dead-beat."    We  shall 

see,  in  section  383,  that  the  same  principle  is  used  to  check  the  rotation 

of  a  watt-hour  meter. 

QUESTIONS  AND  PROBLEMS 

1.   What  limits  the  voltage  which  it  is  practicable  to  use  on  high- 
tension  transmission  lines? 


Fig.  415.  Damping  of 
the  copper  pendulum 
by  eddy  currents. 


410 


ALTERNATING   CURRENTS 


2.  Why  are   the  cables  for  long-distance  transmission  sometimes 
made  of  aluminum  instead  of  copper  ? 

3.  If  a  step-down  transformer  is  to  be  used  to  change  the  voltage 
from  1100  to  220,  what  must  be  the  ratio  of  turns  of  wire  on  the  primary 
and  secondary  coils? 

4.  A  transformer  has  1000  turns  on  the  primary  and  50  turns  on 
the  secondary,  and  the  primary  current  is  20  amperes.     About  how 
much  is  the  secondary  current  ? 

6.  What  generates  the  heat  required  to  weld  the  nails  in  the  experi- 
ment shown  in  figure  411?  Why  does  not  the  copper  wire  S  melt,  as 
well  as  the  tips  of  the  nails  ? 

PRACTICAL  EXERCISES 

1.  Comparative    cost  of  a  bell-ringing  transformer   and  dry  cells. 
Find  the  cost  of  the  transformer  and  the  cost  of  operating  it  including 
"  interest  and  depreciation."     Find  the  cost  of  operating  doorbells  on 
dry  cells.     Which  system  gives  the  better  service? 

2.  Making  a  small  transformer.     Excellent  directions  will  be  found 
in  John  D.  Adams's  Experiments  with  110- volt  Alternating  Current 
(Modern  Pub.  Co.,  N.  Y.). 

373.  Impedance.  If  we  measure  the  resistance  of  the  primary 
coil  of  a  bell-ringing  transformer,  we  find  it  to  be  perhaps 
13  ohms ;  when  we  place  the  transformer  on  a  110- volt  alter- 
nating-current line,  we  might  expect  to  get  -y^-,  or  8.5  amperes. 
But  an  a-c.  ammeter  would  actually  show  only  0.05  amperes 
to  be  flowing  in  the  primary  coil.  Evidently  then  there  is 

something  besides  the  resistance 
which  is  checking  the  alternating 
current.  This  something  which 
checks  the  alternating  current  is 
called  impedance.  In  this  case  the 
impedance  is  -i-^o  or  2200  ohms. 

0-05 

Thus  we  see  that  a  coil  which 
would  be  quickly  burned  out  on  a 
110- volt  d-c.  line  uses  practically 
no  current  on  a  110- volt  a-c.  line. 


Lamp 


Iron  Core 


\A.C. 


Fig.  416.  Lamp  connected  in  series 
with  inductance  on  d-c.  and  a-c. 
circuits. 


Let  an  incandescent  lamp  be  connected  in  series  with  a  coil  which 
has  a  removable  iron  core,  as  shown  in  figure  416, 


ALTERNATING-CURRENT  POWER  411 

Remove  the  core  and  let  a  direct  current  be  passed  through  the 
coil  and  the  lamp.  We  see  that  the  lamp  burns  brightly.  If  we  insert 
the  iron  core  inside  the  coil,  the  brilliancy  of  the  lamp  is  not  in  the 
least  diminished.  If  we  now  remove  the  core  and  connect  the  coil  and 
lamp  to  an  alternating-current  supply  of  the  same  voltage  as  the  direct 
current,  the  lamp  becomes  dim;  and  if  the  iron  core  is  again  inserted 
in  the  coil,  the  dimming  effect  is  still  more  strikingly  shown. 

This  remarkable  choking  down  of  the  alternating  current  is 
caused  by  the  inductance  of  the  coil,  which  sets  up  an  opposing 
e.m.f.,  or  back  voltage,  whenever  the  current  changes. 

374.  Power  in  an  alternating-current  circuit.     In  a  direct- 
current   circuit,  as    we   have    already  learned,  the    power   in 
watts  is  always  equal  to  the  volts  times  the  amperes.     In  an 
alternating-current    circuit    which    is    non-inductive,    such    as 
that  of  an  ordinary  incandescent  lamp,  the  same  rule  holds 
true.     But  in  an  inductive  circuit,  such  as  the  primary  of  a 
bell-ringing  transformer,  we  find  that  the  power,  as  measured  by 
a  wattmeter,  is  less  than  the  product  of  the  volts  times  the 
amperes.     This  fraction  which  the  true  power  is  of  the  apparent 
power  (product  of  volts  times  amperes)  is  called  the  power  factor. 

A-c.  power  (watts)  =  volts  X  amperes  X  power  factor. 
FOR  EXAMPLE,  we  should  expect  the  wattmeter  in  the  case  of  the 
transformer  just  described  to  read  110  X  0.05,  or  5.5  watts;    but  it 
really  indicates  only  4  watts.     Thus  the  power  factor  of  the  trans- 
former primary  coil  is 

True  power      =  _      4  watts  =  ?3  per  cent 

Apparent  power      5.5  volt-amperes 

If  a  circuit  contains  resistance  only,  its  power  factor  is  100  per 
cent;  but  in  an  inductive  circuit  the  power  factor  is  less  than  100 
per  cent.  The  greater  the  amount  of  inductance  in  a  circuit,  the 
lower  will  be  the  power  factor.  In  practice  the  average  value  of  the 
power  factor  on  a  commercial  circuit  with  both  lamps  and  motors  is 
about  85  per  cent. 

375.  Condenser  on  an  alternating-current  circuit.     In  tele- 
phone sets,  the  ringer,  or  bell,  is  operated  by  an  alternating 
current,  and  a  condenser  is  connected  in  series  with  the  bell 


412 


ALTERNATING   CURRENTS 


(Fig.  417)  to  permit  an  alternating  current  to  pass  through  it 
and  to  prevent  the  flow  of  the  direct  current  used  for  talking. 

If  we  connect   an   incandescent  lamp  in  series  with  a  condenser 
(Fig.  418)  to  a  d-c.  line,  the  lamp  is  not  lighted  because  the  circuit  is 

open  between  the  plates  of  the 
condenser.  But  when  we  con- 
nect the  same  circuit  to  an  a-c. 
line,  the  lamp  glows,  even  though 
the  circuit  is  open  between  the 
plates  of  the  condenser. 

The  action  of  a  condenser 
on  an  a-c.  circuit  is  such,  that 
although  no  electricity  flows 
through  the  condenser,  it  does 
flow  into  and  out  of  the  con- 
denser. It  is  this  surging 
back  and  forth  of  the  elec- 
tricity which  causes  the  lamp 
to  glow.  If  we  reduce  the 


Fig.  417.  Diagram  of  connections  in  a 
desk  telephone  set  used  with  common 
battery.  C  is  a  condenser. 


Condenser 


size  of  the  condenser,  no  glowing  is  observed,  because  the  con- 
denser does  not  have  sufficient  capacity. 

We  may  picture  the  action  of  a  condenser  on  an  a-c.  circuit  by 
comparing  it  to  a  box  with  a  diaphragm  in  a  pipe  line,  as  shown  in 
figure  419.  This  box  is  di- 
vided into  two  compart-  D.c. 
ments  C  and  C  by  means 
of  a  rubber  diaphragm  D, 
and  the  two  compartments 
are  connected  to  a  pump  P. 
This  reciprocating  pump  dis- 
places the  water,  first  in 
one  direction,  as  the  piston 
moves  upward,  then  in  the 
other,  as  it  moves  down- 
ward. Thus  the  surging  of 
the  water  back  and  forth  subjects  the  diaphragm  to  a  mechanical 
stress. 

The  pump  corresponds  to  an  a-c.  generator,  the  two  compartments 


Double 
Throw 
Switch 


u 


Fig.   418.      Lamp   connected  in  series 
condenser  on  d-c.  and  a-c.  circuits. 


with 


ALTERNATORS 


413 


Water 

Fig.  419.  Mechanical  analogue  of 
a  condenser  on  an  a-c.  circuit. 


of  the  box  to  the  two  sets  of  plates  in  the  condenser,  and  the  diaphragm 
to  the  dielectric  of  the  condenser. 

Pipe 

When  the  alternating  current 
moves  one  way  in  the  circuit,  one  set 
of  plates  in  the  condenser  becomes 
positively  charged,  the  other  nega- 
tively. When  the  current  reverses, 
the  charges  on  the  condenser  plates 
reverse.  In  the  ordinary  lighting 
.circuit  this  process  of  reversing  takes 
place  120  times  each  second,  so  that 
electricity  flows  rapidly  into  and 
out  of  the  condenser.  Condensers 
play  a  very  important  part  in  radio  telegraphy. 

PROBLEMS 

1.  A  certain  transformer  has  a  primary  coil  with  a  resistance  of 
260  ohms.     What  current  will  it  take  on  a  115- volt  d-c.  line? 

2.  The  same  transformer  on  a   115-volt  a-c.   line  draws  0.0575 
amperes.     What  is  its  impedance? 

3.  The  same  transformer,  when  connected  with  a  wattmeter,  takes 
4.5  watts.     What  is  the  power  factor  of  the  exciting  current  ? 

4.  A  certain  transformer  takes  7.5  watts  from  a  110- volt  a-c.  line 
at  60-per-cent  power  factor.     What  current  does  it  draw  ? 

5.  How  much  power  is  consumed  by  a  coil  on  a  230- volt  a-c.  line, 
when  the  power  factor  is  75  per  cent  and  the  impedance  of  [the  coil  is 
45  ohms? 

376.  Alternators.  When  a  coil  of  wire  is  rotated  in  a  mag- 
netic field,  we  have  seen  (section  339)  that  the  current  changes 
its  direction  every  half-turn.  That  is,  there  are  two  alter- 
nations for  each  revolution  in  a  bipolar  machine.  In  a  direct- 
current  generator  this  alternating  current  is  rectified  by  the 
use  of  a  commutator.  In  the  alternating-current  generator, 
called  an  alternator,  the  current  induced  in  the  armature  is  led 
out  through  slip  rings,  or  collecting  rings  (Fig.  369), 


414 


ALTERNATING  CURRENTS 


The  field  magnet  of  an  al- 
ternator is  usually  an  electro- 
magnet which  is  excited  by 
direct  current  from  a  small 
auxiliary  generator,  called  the 
exciter. 

Since  it  is  only  the  rela- 
tive motion  of  the  armature 
windings   and   field   magnet 
which   is    essential    in    any 
'    generator,    large  alternators 

Fig.  420.     Diagram  of  a  revolving   field    * 

and  stationary  armature.  are  usually  built  with  a  sta- 

tionary armature  and  a  re- 
volving field.  The  revolving  projecting  poles  (N,  S,  N,  S,  in 
figure  420)  sweep  past  the  armature  wires,  which  are  placed 
in  slots  around  the  inner  periphery  of  the  stationary  structure 
A.  The  direct  current  for  exciting  the  field  coils  is  led  in 
through  brushes  which  rub  on  two  insulated  metal  rings.  The 
alternating  current  is  led  directly  from  the  windings  of  the 
stationary  armature  through  cables  to  the  switchboard.  The 
great  advantage  that  the  stationary  armature  has  over  the 
rotating  armature  is  that  the  current  is  generated  in  conductors 
which  do  not  move  and  can  therefore  be  delivered  to  the  exter- 
nal circuit  without  any  sliding  contacts.  It  is  also  easier  to  con- 
struct the  proper  insulation  necessary  for  high  voltages.  Figures 
421  and  422  show  the  revolving  field  and  stationary  armature  of 
a  commercial  alternator  which  is  driven  at  high  speed  by  a 
steam  turbine.  Some  of  these  have  a  speed  of  as  much  as  3600 
r.  p.  m.  Figures  423  and  424  show  the  same  parts  of  an  alter- 
nator which  is  driven  at  slow  speed  by  a  reciprocating  steam 
engine  or  a  water  wheel. 

377.  Cycles  and  phase  of  alternating  currents.  When  a  conductor 
is  moved  past  a  magnetic  TV-pole,  the  induced  e.m.f.  is  in  one  di- 
rection ;  and  when  it  moves  past  an  £-pole,  the  induced  e.m.f.  is  in  the 
opposite  direction.  This  can  be  best  represented  by  the  curved  line 


ALTERNATORS 


415 


Fig.  421. 


Partly  wound  revolving  field  (4  poles)  of  high-speed  alternator 
to  be  used  with  steam  turbines. 


Fig.  422.     Stationary  armature  of  the  alternate 


the 

vhe  case 
ent  is  said 
e  other  by 

show  that, 
t  having  induc- 
alternaing  cur- 
always  retarded  a 
in  amount  behind  the 
ting  voltage  which 
„  its  voltage. 
'3nnect  all  the  stationary 


416 


ALTERNATING   CURRENTS 


bb 

£ 


stru  I 
421  and  . 
a  commerc 
steam  turbi 
r.  p.  m.     Figur 
nator  which  is 
engine  or  a  water 

377.  Cycles  and  ph  | 
is  moved  past  a  magi 
rection ;  and  when  it  mi 
opposite  direction.  Th 


(0     I 

* 

>§§ 
r 


^   o 


SINGLE  AND   POLYPHASE  CIRCUITS 


417 


n 


shown  in  figure  425.     One  complete  wave  is  produced  when  a  wire 
moves  through  a  complete  revolution  in  a  bipolar  machine,  or  from  a 

north  pole  past  a  south 

+30 1— | — |  J^- 1  *L  |    I — HI — I — I — H — H — I — I — I  J^H    pole  to  the  next  north 

pole  in  a  multipolar 
machine,  and  is  called 
a  cycle. 

In  practice  it  is  com- 
mon to  use  for  lighting 
an  alternating   current 
whose  frequency  is  60 
cycles  per  second ;  while  for  power  purposes  25-cycle  currents  are  common. 
A  complete  wave,  or  cycle,  is  called  360  electrical  degrees  by  analogy 
with  the  complete  rev- 

a    bipolar      +30 
Any  point    5f  20 


o-HO 
5  0 
fa' -10 

a- 

-30 


POSITION  OF  LOOP  IN  DEGREES 

Fig.  425.     Curve  of  alternating  e.m.f 


olution  of 
generator, 
or  position  in  the  cycle 
is  spoken  of  as  a  certain 
phase.  When,  for  ex- 
ample, the  cycle  is  half 
completed,  the  phase  is 
said  to  be  180  degrees, 
and  when  the  cycle  is 


>+•} 
•S     o 

fe!  -10 

M 


'/ 


POSITION  OF  ARMASTURE  IN  DEGREES 


Fig.  426. 


Curves  of  two  alternating  currents  which 
differ  in  phase  90°. 


one  fourth  completed,  the  phase  is  90  degrees.     Two  alternating  cur- 
rents of  electricity,  flowing  in  branch   circuits,  may  be  at  different 

phases,  as  represented  in 
figure  426,  where  one  curve 
represents  the  current  in 
one  branch  and  the  other 
curve  the  current  in  the 
other  branch.  In  the  case 
shown,  one  current  is  said 
to  lag  behind  the  other  by 
90  degrees. 

Experiments  show  that, 
in  a  circuit  having  induc- 
tance, an  alternaing  cur- 
rPT1t  ,•„  {,iwj,v(a  r^tarrlorl  a 
' 
certain  amount  behind  the 

alternating  voltage  which 
sets  it  up.     The  alternating  current  lags  behind  its  voltage. 

378.    Single  and  polyphase  circuits.     If  we  connect  all  the  stationary 


Fig.  427.  Diagram  of  a  single-phase  alternator, 
showing  revolving  field  (8  poles)  and  stationary 
armature. 


418 


ALTERNATING  CURRENTS 


*i 


Fig.  428 

nator  with  six  line  wires 


armature  coils  of  a  generator  in 
series,  and  revolve  the  field  as  shown 
in  figure  427,  a  single-phase  alter- 
nating current  is  produced,  whose 
frequency  we  can  determine  by  mul- 
tiplying the  number  of  revolutions  per 
second  of  the  rotor  by  the  number  of 
pairs  of  poles.  To  make  use  of  this 
current  for  any  purpose,  such  as 
electric  lighting,  we  have  simply  to 
cut  this  armature  circuit  at  any 
convenient  point  and  connect  the 

Diagram  of  3-phase  alter-  ends  directly  to  the  mains.     It  will 
be  noticed  that  there  are  as  many 
coils  on  the  armature  as  there  are 
poles  in  the  field  magnet  of  the  single-phase  machine. 

It  has  been  found  more  economical  of  space  to  have  more  than  one 
coil  for  each  pole  of  the  field ;  and  so  we  have  two-phase  and  three- 
phase  machines,  in  which  there 
are  two  or  three  sets  of  coils 
on  the  armature.  In  the  three- 
phase  machine,  which  is  the 
type  most  used  to-day,  the 
three  sets  of  armature  coils 
may  each  be  used  separately  to 

furnish    electricity    for    three    pig   ^      Curveg  of  alternating  currents 
separate    lighting    circuits,   as  jn  a  3.phase  system, 

shown  in  figure  428. 

The  currents  in  the  three  circuits  differ  in  phase  by  120  degrees 
(Fig.  429).  It  will  be  seen  that  the  currents  are  such  that  at  any 
instant  their  sum  is  zero. 


I  II 

Fig.  430.     (I)  The  star  or  Y-connection  and  (II)  the  delta  or  A-connection  on  a 
three-phase  system. 


A    POWER    STATION 


419 


420  ALTERNATING   CURRENTS 

Electrical  engineers  hav.e  invented  two  methods  of  connecting 
apparatus  of  any  sort  to  a  three-phase  circuit,  so  as  to  have  only  three 
live  wires  instead  of  six,  and  thus  to  save  wire.  They  are  the  star 
or  Y-connection  shown  in  figure  430  (I)  and  the  delta  or  A-con- 
nection  shown  in  figure  430  (II).  Most  alternators  have  their  coils. 
Y-connected ;  and  a-c.  motors  are  sometimes  connected  in  star  and 
sometimes  in  delta. 

379.  Use  of  alternators.     The  revolving-armature  type  of 
alternator   is    generally   used   only    in    small   electric-lighting 
stations.     Large   alternators   of   the   revolving-field   type   are 
usually  mounted  on  the  same  shaft  (direct-connected)  with  the 
driving  engine  or  water  wheel.     Alternators  of  very  large  ca- 
pacity are  now  extensively  used  with  steam  turbines.     They 
can  be  comparatively  small  in  size  because  they  are  driven  at 
such  high  speed.     These  alternators  have  a  revolving  field  of 
only  a  few  poles  (sometimes  only  two)  and  a  wide  air  gap  be- 
tween the  armature  core  and  the  field  poles.     Figure  431  shows 
a  30,000-kilowatt  alternator  mounted  on  the  shaft  of  a  steam 
turbine.     In  high-tension  transmission,  the  three-wire  three- 
phase  system  is  commonly  used. 

QUESTIONS 

1.  How  can  the  engineer  at  the  power  house  control  the  frequency 
of  an  alternating  current? 

2.  How  many  revolutions  per  minute  will  an  8-pole  machine  have 
to  make  to  give  a  60-cycle  current? 

3.  What  objection  is  there  to  using  a  25-cycle  current  for  lighting 
purposes  ? 

4.  Draw  a  diagram  to  show  two  alternating  currents  which  differ 
in  phase  by  45  degrees. 

6.  How  much  do  the  two  currents  generated  by  a  two-phase  alter- 
nator differ  in  phase  ? 

380.  Alternating-current    motors.     An    a-c.    generator    can 
be  run  as  a  motor,  provided  it  is  first  brought  up  to  the  exact 
speed  of  the  alternator  which  is  supplying  current  to  it  and  put 
in  step  with  the  alternations  of  the  current  supplied.     Such  a 


ALTERNATING    CURRENT    MOTORS 


421 


machine  is  called  a  synchronous  motor.  Since  it  is  not  self- 
starting,  it  is  not  convenient  for  general  use,  but  is  used  in 
substations  to  drive  d-c.  generators. 

An  ordinary  series  motor,  by  certain  modifications  in  its 
design,  can  be  made  to  operate  on  either  d-c.  or  a-c.  systems. 
These  so-called  a-c.  commutator  motors,  or  single-phase  series 
motors,  are  coming  into  use  for  electric  cars  and  locomotives 


(a) 


Fig.  432.    An  induction  motor  :  (a)  rotor  and  (&)  stator. 

when  an  alternating  current  is  used.  They  are  also  to  be  found, 
in  very  small  sizes,  on  electric  fans  and  on  vacuum  cleaners. 
They  are  labeled  "A-C.  or  D-C."  on  the  name  plates. 

The  a-c.  motor  most  frequently  used  is  the  induction  motor. 
The  distinctive  features  of  this  motor  are  that  the  stationary 
winding,  or  "  stator  "  (Fig.  432  6),  sets  up  a  rotating  magnetic 
field,  and  that  the  rotating  part  of  the  motor,  or  "  rotor,"  is 
built  on  the  plan  of  a  squirrel  cage  (Fig.  432  a).  These  will 
be  discussed  in  turn. 

381.  Rotating  magnetic  field.  To  produce  a  rotating  field,  we  shall 
suppose  that  we  have  two  alternating  currents  of  the  same  frequency, 


422 


ALTERNATING  CURRENTS 


ii  in 


but  differing  in  phase  by  90  degrees  (Fig.  433),  and  that  we  connect 

them  to  two  sets  of  coils  wound  on  the  inwardly  projecting  poles  of  a 

circular  iron  ring,  as  shown  in  figure  434. 

When  the  current  in  line  1  is  at  a  maximum,  it  will  be  seen  from  the 

curves  (Fig.  433)  that  the  current  in  line  2  is  zero.     The  poles  A  and 

AI  are  magnetized,  while  the  poles 
B  and  BI  are  unmagnetized.  The 
magnetic  flux  goes  from  N  to  S,  as 
shown  by  the  arrow.  One  eighth 
of  a  cycle  (45  degrees)  later,  current 
1  has  decreased  to  the  same  value 
as  that  to  which  current  2  has 
increased.  The  four  poles  are  now 
equally  magnetized,  and  the  mag- 
netic flux  takes  the  direction  of  the 
arrow  shown  in  II.  One  eighth  of 


Fig.  433-  Curves  of  two  alternating  cur- 
rents which  differ  in  phase  by  90°, 
with  arrows  showing  magnetic  field. 


a  cycle  (45  degrees)  later,  current  1  ha  dropped  to  zero  and  current  2 
is  at  a  maximum.  This  means  that  the  poles  A  and  AI  are  unmag- 
netized, that  the  poles  B  and  B\  are  magnetized  to  the  maximum, 
and  that  the  flux  passes  from  N  to  S  as  shown  by  the  arrow  in  III. 
If  this  process  is  continued  at  successive  instants  during  a  complete 


I  II  III 

Fig.  434.     A  rotating  magnetic  field  produced  by  two  currents  90°  apart. 

cycle  of  change  in  the  alternating  currents,  we  shall  find  that  the 
arrow  makes  a  complete  revolution.  This  produces  a  rotating  field, 
and  would  cause  a  magnet  to  rotate  with  the  field.  We  should  then 
have  a  little  two-phase  a-c.  motor. 

Figure  435  shows  a  working  model  which  demonstrates  the  rotating 
field  produced  by  a  two-phase  a-c.  system  (right)  and  that  produced 
by  a  three-phase  a-c.  system  (left).  Figure  432  (6)  shows  how  the 
stator  frame  of  a  practical  motor  is  constructed. 


WATT-HOUR   METER 


423 


382.  The  rotor  of  an  induction  motor.  The  rotating  magnet 
can,  of  course,  be  replaced  by  an  electromagnet,  which  is  excited  by 
a  direct  current  from  some  outside  source.  The  rotor  of  a  commer- 
cial a-c.  motor  is,  however,  much  simpler.  It  consists  of  an  iron  core, 
much  like  the  core  of  a  drum  armature,  with  large  copper  bars  placed 


Three-phase  motor 


Fig.  435- 


Working  model  to  demonstrate  the  rotating  field  produced  by  two- 
phase  (right)  and  three-phase  (left)  alternating  currents. 


in  slots  around  the  circumference  and  connected  at  both  ends  to  heavy 
copper  rings.  This  is  called  a  squirrel  cage  rotor  (Fig.  432  (a)). 

When  a  rotor  is  placed  in  a  rotating  magnetic  field,  the  conductors 
on  the  two  sides  and  the  rings  across  the  ends  act  like  a  closed  loop  of 
wire,  and  a  large  current  is  induced,  even  though  the  rotor  has  no 
electrical  connection  with  any  outside  circuit.  This  large  induced 
current  makes  a  magnet  of  the  iron  core,  and  the  field,  acting  on  this 
magnet,  drags  it  around. 

The  rotor  can  never  spin  quite  as  fast  as  the  magnetic  field.  If 
it  did,  there  would  be  no  cutting  of  lines  of  force,  no  currents  would 
be  induced,  and  there  would  be  no  power  available  to  drive  the  rotor 
against  its  load. 

A  squirrel-cage  rotor  is  simple  and  strong,  and  needs  only  to  be  kept 
cool.  This  is  done  by  air  circulated  through  the  core  by  fan  blades. 
The  assembled  machine  is  strong,  compact,  and  almost  "  fool-proof." 
For  these  reasons  the  induction  motor  is  finding  a  wide  field  of  use- 
fulness in  shops  and  factories,  and  even  on  electric  locomotives. 

383.  Watt-hour  meter.  Every  user  of  electricity  is  interested 
in  the  recording  watt-hour  meter,  which  records  on  dials,  like 
those  of  a  gas  meter,  the  number  of  kilowatt  hours  of  elec- 
tricity consumed.  It  is  on  the  readings  of  this  instrument 


424 


ALTERNATING  CURRENTS 


that  the  monthly  bills  are  based.  Figure  436  shows  the  Thom- 
son form  of  watt-hour  meter.  It  is  really  a  little  shunt  motor, 

the  armature   of   which  turns   at  a 

shunt  circuit  ^=L— 1 — ,      speed   proportional   to   the   rate    at 

which  electrical  energy  is  passing 
through  the  meter.  The  armature 
drives  the  recording  dials.  The  field 
of  the  instrument  is  made  by  station- 
ary field  coils  which  are  connected  in 
series  with  the  line.  The  field  strength 
is  therefore  proportional  to  the  cur- 
rent flowing  in  the  main  line.  The 
Fig.  436.  Diagram  of  Thomson's  armature  is  connected  across  the  line, 

and  takes  a  current  proportional  to 

the  voltage  across  the  line.  Therefore,  the  torque  which  turns 
the  armature  is  proportional  to  the  product  of  the  current 
and  the  voltage ;  that  is,  to  the  watts  in  the  line. 


Fig.  437.     Vacuum-tube  rectifier  with  diagram  to  show  the  principle. 

The  inertia  of  such  a  machine  would  make  it  run  too  fast, 
or  fail  to  stop  when  the  current  stopped,  if  it  were  not  for  the 
electric  damping  caused  by  the  rotation  of  an  aluminum  disk 


RECTIFIERS  425 

between  the  poles  of  permanent  magnets.  The  eddy  cur- 
rents generated  in  the  disk  tend  to  retard  its  motion. 

This  type  of  watt-hour  meter  can  be  used  on  either  a  d-c. 
or  an  a-c.  circuit. 

384.  Converting  alternating  current  into  direct  current.  For 
certain  purposes,  such  as  charging  storage  batteries,  it  is  abso- 
lutely necessary  to  use  a  unidirectional  current.  The  method 
of  converting  alternating  current  into  direct  by  means  of  a 
motor-generator  (that  is,  an  a-c.  motor  connected  to  a  d-c. 
generator)  is  used  for  large  power  purposes.  But  for  charging 
automobile  batteries,  the  vacuum-tube  rectifier  ("  Tungar  ") 
is  much  more  convenient.  While  this  type  of  rectifier  (Fig. 
437)  gives  a  unidirectional  current,  yet  it  does  not  give  an 
absolutely  steady  current. 

It  consists  of  an  evacuated  glass  bulb  containing  a  tungsten  fila- 
ment F  heated  to  incandescence  by  an  alternating  current,  and  has 
a  carbon  electrode  A  introduced  through  the  top  of  the  bulb.  The 
bulb  itself  is  filled  with  inert  gas  at  low  pressure.  The  tungsten  fila- 
ment is  connected  in  the  secondary  circuit  of  a  transformer,  which  is 
part  of  the  outfit,  and  when  heated  to  incandescence  emits  electrons 
(negative  electricity).  If  this  filament  is  negative  with  respect  to  a 
near-by  anode,  the  rarefied  gas  in  the  bulb  is  ionized  and  thus  becomes 
a  conductor  of  electricity.  The  filament  is  also  connected  to  one  ter- 
minal of  the  a-c.  line,  and  the  graphite  (carbon)  electrode  A  is  con- 
nected to  the  other  terminal.  During  the  half-cycle  in  which  the 
graphite  electrode  is  positive  and  the  filament  is  negative,  current 
passes  through  the  bulb,  because  of  the  ionizing  action  of  the  electrons. 
During  the  other  half -cycle,  when  the  graphite  electrode  is  negative, 
the  gas  remains  nonconducting,  because  the  electrons  cannot  escape 
from  the  filament.  Thus  the  current  passes  through  the  valve  during  each 
alternate  half-cycle  from  the  graphite  to  the  tungsten  filament.  We  have, 
then,  in  the  circuit  of  the  bulb  a  pulsating  unidirectional  current,  which 
is  suitable  for  charging  storage  batteries. 

PRACTICAL  EXERCISE 

Making  an  electrolytic  rectifier.  A  simple  form  of  rectifier  consists 
of  four  jars,  each  containing  a  solution  of  ammonium  phosphate,  a  strip 
of  sheet  lead,  and  a  strip  of  aluminum.  See  Adams's  Experiments  with 
110-volt  Alternating  Current  (Modern  Pub.  Co.). 


426 


ALTERNATING  CURRENTS 


SUMMARY  OF  PRINCIPLES  IN  CHAPTER  XVIII 

In  a  transformer : 

Voltage  on  primary  turns  of  primary 

Voltage  on  secondary      turns  of  secondary 

In  an  alternator : 

Frequency  =  revolutions   per   second  X  number  of  pairs  of 
poles. 

A-c.  power  =  amperes  X  volts  X  power  factor. 
Power  factor  is  usually  less  than  one. 


Steel  su 


QUESTIONS 

1.  The  iron  case  of  a  transformer  is  often  corrugated.     Why  ? 

2.  Why  must  the  "dielectric  strength"  of  the  oil  used  in  trans- 
formers be  carefully  tested  ? 

3.  In  long-distance  transmission  of  power  by  high-tension  lines, 
the  wires  are  often  supported  on  steel  towers  75  feet  above  the  ground, 

and  the  company  gets  a  right  of  way  or  a 
strip  of  land  100  feet  wide  over  which  to 
run  its  wires.  Why  these  precautions  ? 

4.  What   is    gained    by    making    the 
armature  of  a  big  alternator  stationary, 
and  rotating  the  field  ? 

5.  How   could  an   induction    coil   be 
used  as  a  step-up  transformer? 

6.  What  advantages  have  steel  towers 
over  wooden  poles  for  holding  up  high- 
tension  wires  ? 

7.  What  advantages  has  the  suspen- 
sion-type of  insulator  (Fig.  438)  for  high- 
voltage  transmission  lines? 

8.  What   type  of  alternator   is   used 
with  a  reciprocating  steam  engine  ?  Why  ? 

9.  What  reasons  have  led  to  the  fact 


Fig.  438.  Suspension-type  of 
insulator  used  on  high-volt- 
age lines. 


that  a  very  large  percentage  (perhaps  95  per  cent)  of  all  the  electrical 
power  generated  in  this  country  to-day  in  central  stations  is  alternat- 
ing current? 


CHAPTER  XIX 


SOUND 

What  makes  sound  —  what  carries  sound  —  velocity  of 
sound  —  water  waves  —  velocity,  wave  length,  and  frequency 
—  longitudinal  waves  —  sound  waves  —  loudness  and  dis- 
tance —  directing  sound  —  finding  the  direction  of  sound  — 
reflecting  sound  —  sound  in  rooms  —  musical  tones  —  inten- 
sity, pitch,  and  quality  —  resonators  —  overtones  —  photo- 
graphing sound  waves  —  beats  —  the  musical  scale  — 
stringed  instruments  —  wind  instruments  —  membranes  — 
the  phonograph. 

385.  What  makes  sound  ?  When  a  bell  rings,  we  see  the 
hammer  or  clapper  hit  the  bell,  and  hear  the  sound  which  it 
makes.  If  we  hold  a  pencil  against  the  edge  of  the  bell  just 
after  it  has  been  struck,  we  find  that 
the  metal  is  moving  to  and  fro  very 
rapidly.  When  a  guitar  string  is 
plucked,  it  gives  forth  a  note  which 
we  can  hear,  and  at  the  same  time  we 
can  see  that  the  string  looks  broader 
than  when  at  rest.  We  conclude  that 
the  string  is  vibrating  or  oscillating 
back  and  forth.  When  we  strike  a 
tuning  fork  and  hold  it  near  the  ear, 
we  hear  a  note,  and  if  we  touch  the 
fork  to  the  lips,  we  feel  its  vibratory 
motion. 


Fig-    439-      Vibration    of 
tuning  fork  made  visible. 


To  make  visible  the  vibration  of  a  tuning  fork,  let  us  touch  it  to 
a  light  glass  bubble  suspended  on  a  thread  (Fig.  439).  The  bubble  is 
set  violently  in  motion. 

427 


428 


SOUND 


Fig.  440.     Curve  traced   by   a  vibrating 
fork  on  a  smoked  glass. 


Another  way  to  show  the  vibratory  motion  of  a  fork  is  to  attach  a 
point  of  stiff  paper  to  one  prong.  Let  us  set  such  a  fork  in  vibration  and 
draw  a  piece  of  smoked  glass  under  it  (Fig.  440).  The  curve  traced  is 
easily  made  visible  by  putting  white  paper  behind  the  glass. 

Whenever  we  look  for  the  source  of  a  sound,  we  find  that 
something  has  been  set  in  motion.  It  may  be  that  some- 
thing has  fallen,  a  bell  has  been  struck,  a  whistle  has  been 

blown,  or  someone  has 
shouted;  always  something 
has  been  set  vibrating, 
which  has  caused  the  sensa- 
tion of  sound. 

386.   What  carries  sound? 

Ordinarily  the  air,  which  is  everywhere  about  us,  brings 
sound  to  our  ears.  To  make  this  evident  let  us  try  the  fol- 
lowing experiment. 

Let  us  place  an  alarm  clock  on  a  felt  cushion  under  the  receiver  of 
a  good  vacuum  pump,  as  shown  in  figure  441.  If  we  set  the  clock  so 
that  the  bell  rings  intermittently,  and  then  pump  out  the  air,  we  find 
that  the  sounds  become  fainter  and  fainter. 
When  we  let  the  air  in  again,  the  bell  sounds 
as  loud  as  at  first.  It  seems  probable  that 
the  bell  would  become  quite  inaudible  if  we 
could  get  a  perfect  vacuum,  and  if  no  sound 
were  conducted  out  by  the  supporting  base. 

We  know  that  both  heat  and  light  can 
traverse  a  vacuum,  as  in  the  case  of  the 
electric-lamp  bulb ;  but  we  see  from  this 
experiment  that  sound  does  not  traverse  a 
vacuum. 

It  can  be  shown  that  other  gases  besides  air  carry  sound,  and 
that  liquids  and  solids  are  even  better  carriers  of  sound  than 
gases.  For  example,  if  one  holds  one's  ear  under  water  while 
some  other  person  hits  two  stones  together  a  short  distance  away, 
the  sound  is  heard  very  distinctly.  It  is  also  a  familiar  fact  that 
one  can  hear  a  train  a  long  distance  away  by  putting  one's  ear 


Fig.  441.  Sound  is  not 
carried  through  a 
vacuum. 


HOW  FAST  DOES  SOUND  TRAVEL? 


429 


close  to  the  steel  rail.  Loud  sounds,  like  those  of  cannon,  or 
of  volcanic  eruptions,  can  be  heard  at  a  distance  of  several  hun- 
dred miles  by  putting  one's  ear  to  the  ground. 

To  show  that  liquids  transmit  sound,  let  us  put  the  stem  of  a  tuning 
fork  into  a  hole  bored  in  a  large  cork.  If  we  set  the  fork  in  vibration, 
it  is  hardly  audible ;  but  if  we  hold  it  with  the  cork  resting  on  the  sur- 
face of  a  glass  of  water  which  stands  on  a 
resonating  box  (Fig.  442),  we  hear  it  dis- 
tinctly. The  sounds  seem  to  be  coming 
from  the  box.  This  experiment  shows 
that  the  vibration  of  the  tuning  fork  is 
transmitted  through  the  cork  and  the 
water  to  the  air  in  the  room. 

To  show  that  solids  transmit  sound, 
we  may  hold  one  end  of  a  long  wooden 
stick  against  a  door,  and  rest  a  vibrat- 
ing tuning  fork  on  the  other  end ;  the 
sound  of  the  fork  seems  to  be  coming 
from  the  door.  The  wooden  stick  here 
serves  as  the  sound  carrier  and  trans- 
mits the  vibration  of  the  fork  to  the 
door. 


Fig.    442.     Sound   of   fork  is 
transmitted  by  water  to  box. 


So  we  conclude  that  solids,  liquids,  and  gases  may  serve  as 
carriers  of  sound. 

387.  How  fast  does  sound  travel?  In  an  ordinary  room 
one  is  not  aware  that  it  takes  any  appreciable  time  for  sound  to 
travel  from  its  source  to  one's  ears ;  but  in  a  large  hall,  or  out- 
doors, one  often  hears  an  echo,  which  shows  that  sound  does 
take  time  to  travel  to  a  reflecting  surface  and  back.  During 
a  thunder  shower  we  hear  the  roll  of  the  thunder  after  we  see 
the  flash.  The  farther  away  the  lightning  discharge  is,  the 
longer  the  interval  between  seeing  the  flash  and  hearing  the 
rumble.  Everyone  has  doubtless  seen  the  steam  from  a  dis- 
tant whistle,  and  then  later  heard  the  whistle.  So  there  is  no 
doubt  that  sound  travels  much  more  slowly  than  light. 

One  way  to  measure  how  fast  sound  travels  is  to  have  a  cannon 
discharged  on  a  distant  hill  and  measure  the  time  between  see- 


430  SOUND 

ing  the  flash  of  the  cannon  and  hearing  its  report.  In  such 
an  experiment,  which  was  performed  by  two  Dutch  scien- 
tists in  1823,  two  cannons  were  set  up  on  hills  about  eleven 
miles  apart,  and  observations  were  made  first  from  one  hill 
and  then  from  the  other,  to  eliminate  the  error  due  to  wind. 
Their  result  was  remarkably  near  the  truth,  considering  the 
instruments  they  had.  Since  then,  several  determinations  of 
the  velocity  of  sound  in  air  have  been  made,  which  show  that 
at  0°  C.  and  76  centimeters  pressure  the  velocity  of  sound  is 
1087  feet  (or  331  meters)  per  second.  The  speed  of  sound  in 
water  is  about  4.5  times  the  speed  in  air,  and  in  steel  it  is  more 
than  15  times  as  great  as  in  air.  It  has  also  been  found  that  the 
speed  of  sound  in  air  increases  about  2  feet  (or  0.6  meters) 
per  second  for  each  degree  centigrade  rise  in  temperature. 
For  many  practical  purposes  it  is  enough  to  remember  that 
sound  travels  in  air  about  1100  feet  per  second. 

PROBLEMS 

(Assume  that  the  time  taken  by  light  to  travel  ordinary  distances  is  negligible.) 

1.  A  steam  whistle  is  heard  2.6  seconds  after  the  steam  is  seen.     How 
far  away  is  the  whistle  ?     Assume  the  temperature  to  be  15°  C. 

2.  A  man  sees  a  hammer  strike  a  bell  a  mile  away  every  2  seconds. 
What  is  the  interval  between  the  sounds  of  the  successive  strokes? 

3.  On  a  hot  summer  day,  when  the  temperature  is  30°  C.,  the  flash 
of  a  gun  is  seen  2  miles  away.     How  long  after  the  flash  will  the  report 
of  the  gun  be  heard  ? 

4.  A  stone  is  dropped  from  the  top  of  the  Woolworth  Building  in 
New  York  City,  which  is  750  feet  high.      The  temperature  is  68°  F. 
How  long  before  a  man  on  top  would  hear  the  sound  of  the  stone  as 
it  struck  the  pavement?     (The  time  includes  the  time  for  the  stone 
to  fall  and  for  the  sound  to  return.) 

5.  If  an  experiment  shows  that  sound  travels  in  water  4814  feet  per 
second  at  14°  C.,  how  many  times  as  fast  does  sound  travel  in  water 
as  in  air  at  this  temperature? 

6.  A  lightship  is  equipped  with  a  bell  under  water  and  with  a  foghorn. 
The  captain  of  a  vessel  receives  the  under-water  signal  in  a  telephone 


SOUND  IS  A    WAVE   MOTION 


431 


receiver  (Fig.  443)  4  seconds  before  he  hears 
the  whistle.  Assuming  that  sound  travels 
1100  feet  per  second  in  air  and  4800  feet 
per  second  in  water,  compute  the  distance  of 
the  captain  from  the  lightship. 

7.  If  the  noon  signal  is  given  by  a  gun 
5  miles  away,  how  much  allowance  must 
be  made  when  the  temperature  is  80°  F.  ? 

8.  A  steel  rail  is  struck  and  the  blow  is 
heard  through  the  rail  in  0.2  seconds,  and 
then  through  the  air  2.8  seconds  later.     As- 
sume  the  temperature  to  be  20°  C.    How 
many  feet  distant    was  the   blow   struck? 
What  was  the  velocity  of  the  sound  in  the  rail  ? 


Fig.  443.  Submarine  tele- 
phones attached  to  a 
ship's  sides. 


PRACTICAL  EXERCISE 

Measuring  the  velocity  of  sound.  Repeat  the  experiment  described 
in  section  387,  using  a  toy  cannon  and  a  stop  watch.  Get  the  distance 
from  a  large  scale  map.  Record  the  temperature. 

388.  Sensation  of  sound.     We  have  been   considering  the 
transmission  of  "  sound  "  through  gases,  liquids,  and  solids, 
although  we  know  that  it  is  merely  a  sort  of  motion  which 
is  transmitted.     Ordinarily  we  find  it  hard  to  think  of  sound 
without  thinking  of  an  ear  to  hear  it.     Thus  we  find  people 
asking  whether  a  waterfall  in  a  very  remote  part  of  the  earth, 
never  visited  by  man  or  animal,  makes  any  sound.     Evidently 
there  are  two  things  which  are  called  "  sound,"  the  vibrations 
and  the  sensation  they  produce  when  they  strike  against  the 
tympanum,  or  eardrum.     The  study  of  what  happens  in  the 
ear  and  brain  is  properly  left  to  physiology  and  psychology.     In 
physics  we  shall  consider  only  the  vibrations  in  the  air  or  other 
transmitting  medium,  and  shall  refer  to  them  when  we  say 
"  sound."     In  this  sense  the  waterfall  makes  just  as  much 
sound  whether  there  is  an  ear  to  hear  it  or  not. 

389.  Sound  is  a  wave  motion.     Evidently  nothing  material 
(that  is,  weighable)  travels  from  the  source  of  a  sound  to  the 
ear;    otherwise,  how  did  the  sound  of  the  electric  bell  under 


432 


SOUND 


Fig.  444.     Apparatus  for  projecting  on  the  ceiling 
water  waves  illuminated  from  below. 


the  bell  jar  get  through  the  glass?  This  and  other  facts  point 
unmistakably  to  the  conclusion  that  what  is  transmitted  is 
merely  a  vibration,  or  mode  of  motion,  called  a  wave. 

390.  Water  waves.  Since  sound  waves  are  usually  invisible, 
we  shall  start  with  a  study  of  water  waves.  When  a  stone 

is  dropped  into  a 
smooth  pond,  a  dis- 
turbance is  produced 
which  extends  over  the 
surface  of  the  water  in 
circles  centered  at  the 
place  where  the  stone 
struck.  The  water  is 
pushed  down  and  aside 
by  the  stone,  forming 
a  circular  ridge,  which 
expands  into  a  larger 

circle  and  is  followed  by  a  second  circular  ridge,  which  ex- 
pands, and  so  on.  The  result  is  that  the  surface  is  soon  cov- 
ered with  a  series  of  circular  crests,  which  are  separated  by 
circular  troughs,  all  moving  away  from  the  center  of  the  dis- 
turbance. 

These  water  waves  can  be  projected  on  the  ceiling  by  means  of  a 
shallow,  water-tight  box  with  wooden  sides  and  a  plane  glass  bottom. 
The  box  is  supported  so  that 
light  may  be  thrown  on  it  from 
below  (Fig.  444).  Water  is 
poured  in  to  a  depth  of  a 
quarter  of  an  inch,  and  the 
light  which  passes  through  the 
box  is  received  on  the  ceiling.  When  a  wave  is  set  up  in  the  water, 
shadows  corresponding  to  the  wave  fronts  will  be  seen  on  the  ceiling. 

The  surface  of  a  water  wave  may  be  represented  by  the 
curved  line  shown  in  figure  445.  The  stationary  points,  A,  B, 
C,  D,  etc.,  are  called  the  nodes  ;  the  intervening  spaces  are  called 
the  loops  or  internodes.  The  water  between  nodes  oscillates 


Fig.  445.     Cross  section  of  a  water  wave. 


TRANSVERSE  AND  LONGITUDINAL   WAVES        433 

up  and  down ;  when  it  is  up,  it  forms  a  crest,  and  when  it  is 
down,  a  trough.  A  crest  and  trough  together  form  a  wave,  as 
from  A  to  C,  or  B  to  D.  The  wave  length  I  is  measured  hori- 
zontally from  any  point  on  one  wave  to  the  corresponding 
point  in  the  next  wave.  Corresponding  points  are  called  points 
in  the  same  phase.  The  amplitude  d  of  the  wave  vibration  is 
half  the  vertical  distance  from  trough  to  crest. 

391.  Relation  between  velocity,  wave  length,  and  frequency. 
In  the  case  of  the  waves  started  by  throwing  a  stone  into  a 
quiet  pool,  we  know  that  while  the  circular  waves  grow  larger 
and  larger,  any  particular  crest  seems  to  move  out  radially 
until  it  reaches  the  bank  or  dies  away.     The  distance  which  a 
crest  travels  in  one  second  is  called  its  velocity  (v).    The  number 
(n)  of  crests  passing  a  fixed  point  in  one  second  is  called  the  fre- 
quency.    A  moment's  thought  will  show  that  the  relation  be- 
tween the  wave  length,  velocity,  and  frequency  of  a  wave  must  be 

Velocity  =  frequency  x  wave  length, 
or  v  =  nl. 

It  should  be  remembered  that  it  is  only  the  wave  form  that  travels 
over  the  surface  of  the  water,  not  the  water  particles  themselves. 
Thus  if  we  float  a  cork  or  a  toy  boat  on  a  pool  over  whose  surface  waves 
are  passing,  the  cork  or  boat  merely  bobs  up  and  down  as  a  wave  passes, 
but  is  not  carried  along  with  it. 

392.  Transverse   and   longitudinal   waves.    An  easy  way  of 
illustrating  wave  motion  is  to  fasten  one  end  of  a  piece  of  rubber 
tubing  about  20  feet 

long  to  a  hook  in 

the    wall.      If    we 

take    the    free    end  Fig.  446.    Transverse  waves  in  a  rubber  tube. 

in  the  hand,  we  can, 

by  a  quick  shake,  send  a  wave  along  the  tube  (Fig.  446).     If  a  single 

depression  is  sent  along  the  tube  to  the  fixed  end,  it  is  reflected  and 

returns  as  an  elevation ;  in  like  manner  a  single  elevation  sent  along  the 

tube  comes  back  as  a  depression. 

In  the  case  of  water  waves  and  of  the  waves  in  a  tube  or 
cord,  the  particles  of  water  or  tubing  oscillate  up  and  down, 


434  SOUND 

while  the  disturbance  moves  horizontally.     Such  waves   are 

called  transverse  waves. 

A  second  kind   of   wave   motion  takes  place  in  substances 

such  as  gases  and  wire  springs,  which  are  elastic  and  com- 
pressible. This  kind  of  wave  can  be  studied  by 
letting  a  coil  of  wire  represent  the  substance  through 
which  such  waves  are  transmitted. 

Figure  447  represents  a  spring  whose  turns  are  large  and 
one  of  whose  ends  is  supported  from  a  hook  in  the  ceiling. 
If  we  compress  a  few  turns  near  the  lower  end,  these  move 
slightly  and  compress  those  just  above ;  and  these  in  turn 
squeeze  together  the  turns  still  farther  up.  Thus  a  pulse, 
or  wave,  goes  along  the  spring. 

Next  let  the  lower  end  of  the  spring  be  given  a  quick 
pull,  so  that  the  turns  near  by  are  drawn  apart  for  an  in- 
stant. Then  the  adjacent  turns  will  be  pulled  apart, 
one  after  another,  until  this  disturbance  reaches  the 
top.  Thus  it  is  seen  that  any  push  or  pull  given  to  the 
spring  at  one  end  is  transmitted  as  a  push  or  pull  to  the 
Fig.  447.  other  end. 

nafwaves       Waves   of  this   sort,  in   which  the    particles   of 
in  a  verti-  the   transmitting   material   move    back   and   forth 
ing'  in  the  direction  of  the  advance  of  the  wave,  are 
called  compression  or  longitudinal  waves. 

393.  Longitudinal  waves  in  solids.  Not  only  springs,  but 
gases  and  even  solids  like  steel,  transmit  longitudinal  waves. 

If  we  clamp  a  steel  rod  in  the  middle  and  rub  it  lengthwise  with  a 
cloth  dusted  with  rosin,  a  clear,  ringing  sound-may  be  produced.  That 
the  rod  has  been  set  in  longitudinal  vibration  can  be  shown  by  a  little 
ivory  ball  hung  by  a  cord  so  as  to  rest  against  the  end  of  the  rod.  When 
the  rod  is  vibrating,  the  ball  swings  out  violently  (Fig.  448). 

A  mechanical  illustration  of  the  fact  that  a  push  or  pull  may 
travel  a  long  distance,  although  the  individual  particles  move 
only  very  minute  distances,  is  shown  in  figure  449. 

The  apparatus  consists  of  several  glass-hard  steel  balls  hung  in  line 
so  that  they  just  touch  each  other.  If  we  pull  aside  the  first  ball 
and  let  it  fly  back  against  the  line  of  balls,  the  ball  it  strikes  does  not 


SOUND   WAVES 


435 


Ball   set  in    vibration   by   longitudinal 
waves  in  the  rod. 


seem  to  move,  nor  the  next  one.  In  fact,  none  seem  to  be  affected 
by  the  blow  except  the  ball  on  the  opposite  end,  which  flies  out  about 
as  far  as  the  first  ball  fell.  Since  steel  is  very  elastic,  the  impact  to  the 
first  ball  is  handed  along 
from  ball  to  ball  until  it 
reaches  the  end  one.  It 
is  as  though  a  push  were 
given  to  the  first  of  a 
column  of  boys  stand- 
ing in  line.  It  is  trans- 
mitted along  the  line,  and 
the  last  boy  is  pushed 
over. 

394.   Soundwaves. 

We  think  of  the  air  F»g-  448. 
in  sound  waves  as 
vibrating  to  and  fro  in  the  direction  of  propagation  like  the 
turns  of  a  spring;  that  is,  sound  waves  are  longitudinal,  or 
compression,  waves,  made  up  of  alternate  condensations  and 

rarefactions.  Just  as  a  stone 
thrown  into  a  pool  makes 
waves  which  spread  out  in 
ever  widening  concentric 
circles,  so  we  think  of  a  bell 
as  sending  out  spherical 
waves.  These  are  made  up 
of  alternate  spherical  shells 
of  compressed  and  of  rare- 
fied air,  traveling  out  in 
every  direction  through 
space. 

To  form  a  picture  of  a 
sound  wave  traveling  through 
a  speaking  tube,  let  us  imagine  that  the  spiral  spring  of  the  model 
(Fig.  447)  is  replaced  by  a  column  of  air,  which  has  a  tuning 
fork  at  one  end,  giving  little  pulses  to  the  air  column,  while 
an  eardrum  at  the  other  end  receives  these  pulses  (Fig.  450). 


Fig.  449.     Illustrating  how  sound  travels 
from  particle  to  particle. 


436 


SOUND 


Fig.  450. 


Diagram"  to  show  how  sound  waves  may 
be  represented  by  a  curve. 


The  successive  condensations  and  rarefactions  of  the  air  are 
indicated  by  c  and  r  in  A'B'.  The  disturbance  travels  from 
the  fork  to  the  ear,  but  the  intervening  air  at  any  point  merely 
oscillates  a  very  little  to  and  fro.  The  curve  in  figure  450  is 
a  graphical  representation  of  these  sound  waves,  in  which  the 
crests,  1-2,  3^,  etc.,  represent  condensations  or  compressions, 
and  the  troughs,  2-3,  etc.,  represent  rarefactions.  The  ampli- 
tude of  the  wave 
corresponds  to  the 
distance  each  particle 
of  air  moves  to  and 
fro  from  its  original 
position.  A  sound 
wave  includes  a  com- 
plete  crest  and 
trough,  —  that  is,  a 
condensation  and 
rarefaction,  —  and 
the  distance  between  two  corresponding  points  in  any  two 
adjacent  waves  is  called  the  wave  length. 

Since  the  same  relation  between  velocity,  wave  length,  and 
frequency  holds  for  sound  waves  as  for  water  waves,  we  can 
easily  compute  the  length  of  a  sound  wave. 

FOR  EXAMPLE,  suppose  a  tuning  fork  is  giving  256  vibrations  each 

/second,  and  that  the  velocity  of  sound  at  20°  C.  is  1127  feet  per  second. 

Then  the  wave  length  is  1127  feet  divided  by  256,  or  about  4.4  feet. 

To  picture  a  sound  wave  spreading  through  the  open  air, 
we  may  imagine  a  great  number  of  spiral  springs  radiating 
out  from  a  common  center  at  the  source  of  the  sound,  all  re- 
ceiving an  impulse  at  the  same  time. 

PROBLEMS 

(Assume  that  the  temperature  is  0°  C.  unless  otherwise  stated.) 

1.  An  A  tuning  fork  on  the  international  scale  makes  435  vibrations 
per  second.  What  is  the  length  of  the  sound  wave  given  out  ? 


INTENSITY   OF  SOUND 


437 


2.  A  vibrating  string  gives  out  sound  waves  2  feet  long.     What  is 
the  frequency  of  the  waves  ? 

3.  The  time  required  for  one  sound  wave  to  pass  a  given  point  is 
found  to  be  0.0025  seconds.     What  is  the  length  of  the  wave? 

4.  A  bell  whose -frequency  is  150  vibrations  per  second  is  sounded 
under  water,  in  which  sound  travels  at  the  rate  of  4800  feet  per  second. 
Find  the  wave  length  produced  by  the  bell. 

6.  If  the  highest  tone  which  the  ear  can  recognize  makes  30,000 
vibrations  per  second,  what  is  the  shortest  wave  which  the  ear  ap- 
preciates ? 

6.  If  a  certain  organ  pipe  at  20°  C.  has  a  pitch  of  521  vibrations 
per  second,  what  is  the  pitch  (frequency)  of  the  same  pipe  at  10°  C.? 

7.  Find  the  vibration  frequency  of  a  violin  string  that  sends  out 
sound  waves  1  meter  long  at  15°  C. 

8.  A  tuning  fork  makes  1024  vibrations  per  second,  and  the  length 
of  the  sound  wave  given  off  is  32  centimeters,     (a)    Find  the  velocity 
of  the  sound.     (6)    Find  the  temperature  on  the  centigrade  scale. 

395.  Intensity,  or  loudness,  of  sound.  It  must  always  be 
remembered  that  when  an  electric  bell  is  struck,  the  sound  is 
heard  in  all  directions  ; 
this  means  that  sound 
waves  spread  out  in  all 
directions,  as  shown  in 
figure  451.  As  the  dis- 
tance from  the  source 
increases,  the  energy  in 
each  wave  spreads  out 
over  more  surface,  and 
so  the  intensity  of  the 
sound  decreases.  For  example,  a  bell  10  feet  away  sounds  one 
fourth  as  loud  as  the  same  bell  5  feet  away,  and  if  15  feet 
away,  it  sounds  one  ninth  as  loud  as  when  5  feet  away.  This 
is  because  the  energy  of  each  wave  must  be  imparted  to  nine 
times  as  many  particles  at  a  distance  of  15  feet  as  at  a  dis- 
tance of  5  feet.  In  general,  the  intensity  of  sound  varies  in- 
versely as  the  square  of  the  distance. 


451- 


Sound  waves  spread  out  in  all  direc- 
tions from  the  bell. 


438  SOUND 

If  one  ascends  to  a  high  altitude,  as  on  a  mountain  top  or 
in  a  balloon  or  airplane,  the  air  becomes  less  dense  and  hence 
not  so  good  a  carrier  of  sound.  This  makes  it  difficult  to 
transmit  sounds.  In  general,  the  intensity  of  sound  depends 
on  the  density  of  the  medium  through  which  the  sound  is  trans- 
mitted. 

396.  Speaking  tubes  and  megaphones.     The  speaking  tubes  used 
to  connect  rooms  in  buildings  and  ships  serve  to  prevent  the  spread- 
ing out  of  sound  waves  in  all  directions,  and  so  the  sound  is  heard 
with  almost  its  original  intensity  at  the  distant  point.     Sharp  bends  in 
such  tubes  should  be  avoided,  as  they  cause  reflected  waves,  which 
dissipate  some  of  the  energy. 

In  the  megaphone  the  sound  waves  which  come  from  the  mouth  are 
not  permitted  by  the  walls  of  the  instrument  to  spread  out  in  all  direc- 
tions. In  this  way  the  energy  of  the  voice  is  sent  largely  in  one  di- 
rection. 

397.  Finding  the  direction  of  sound.     A  listener  can  usually 
locate  very  accurately,  even  when  blindfolded,  the  direction 
from  which  a  sound  comes.     The  only  exception  is  that  sounds 
which  are  directly  in  front  of,  above,  or  behind  him  are  readily 
mistaken  one  for  the  other.     In  each  of  these  cases,   sound 
from  the  source  reaches  his  right  and  his  left  ear  at  the  same 
time,  while  other  sounds  reach  one  ear  a  little  sooner  than  the 
other  because  of  the  shorter  path  traveled ;  thus  it  seems  reason- 
able to  suppose  that  it  is  the  time  interval  between  impingement 
on  the  nearer  and  on  the  more  distant  ear  that  gives  us  our 
sense  of  sound  direction. 

It  has  been  found  that  if  two  equally  long  rubber  tubes  are  put, 
one  in  each  ear,  and  if  the  further  end  of  one  tube  is  scratched  with 
a  needle  a  few  hundredths  of  a  second  sooner  than  the  other,  a  blind- 
folded listener  seems  to  hear  only  one  scratch  and  assigns  to  it  a 
perfectly  definite  direction  on  the  side  of  the  head  corresponding  to 
the  earlier  scratch. 

These  facts  were  made  use  of  during  the  World  War  for  locating 
submarines.  Two  little  rubber  bulbs  on  the  ends  of  a  cross  arm  10 
or  12  feet  long  under  the  ship  served  as  widely  separated  ears.  From 
one  a  tiny  speaking  tube  led  to  the  right  ear  of  the  observer,  while 


REFLECTION  OF  SOUND 


439 


Fig.  452.  Diagram  of 
apparatus  used  to 
detect  the  direction 
of  a  submarine. 


the  other  bulb  was  similarly  connected  to  his  left  ear  (Fig.  452).  When 
a  sound  came  through  the  water,  the  cross  arm  was  rotated  around  a 
vertical  axis  until  the  sound  seemed  to  the  observer  to  be  squarely  in 
front  of  him.  Then  a  perpendicular  to  the  cross 
arm  indicated  the  direction  of  the  submarine 
within  1°  or  2°. 

A  similar  device  used  near  the  bow  of  an 
ocean  liner  enables  a  seaman  to  determine  the 
direction  from  which  the  sound  from  the  propeller 
at  the  stern  seems  to  come  after  it  has  been 
reflected  from  the  bottom  of  the  ocean.  A 
simple  calculation,  involving  the  length  of  the 
ship,  then  gives  the  depth,  and  makes  sound- 
ings unnecessary  when  the  vessel  is  approaching 
shallow  water  (Fig.  453). 

Big  guns  were  located  in  a  similar  way 
during  the  war;  except  that  little  electrical 
"  ears  "  were  put  out  half  a  mile  apart  behind 
the  battle  front,  and  the  interval  between  the 

arrival  of  the  boom  of  the  gun  at  one  "ear"  and  at  another  was  re- 
corded by  sensitive  galvanometers  on  a  moving  film.  This  was  called 
sound-ranging. 

398.  Reflection 
of  sound.  Just  as 
any  elastic  body, 
like  a  rubber  ball, 
bounds  back  when 
thrown  against  a 
brick  wall,  or  a 
water  wave  is 
turned  back  by  a 
stone  embankment, 
so  a  sound  wave  is 
turned  back,  or  re- 
flected, when  it 

strikes  against  another  body,  such  as  a  building,  cliff,  or  wooded 
hillside,  or  even  a  cloud.  The  returning  wave  is  called  an  echo. 
The  reflecting  surface  has  to  be  20  or  25  yards  distant,  for  the  echo 


Fig-  453-  A  method  of  finding  depth  of  water  by 
determining  the  direction  of  sound  from  ship's 
propellers. 


440 


SOUND 


to  be  distinct  from  the  original  sound.  The  greater  the  dis- 
tance, the  longer  is  the  time  before  the  reflected  wave  strikes 
the  ear,  and  therefore  the  more  striking  the  echo  becomes. 
When  we  have  parallel  walls,  as  in  a  narrow  canon,  or  objects  at 
different  distances,  the  echo  is  multiple  or  repeated,  which 
means  that  the  same  sound  is  heard  several  times.  For  example, 
the  roll  of  thunder  results  in  part  from  the  reflection  of  the  sound 
from  a  succession  of  mountains  or  clouds. 

The  following  experiment  shows  that  sound  waves,  like  light  waves, 
are  reflected  by  curved  surfaces.  Jf  two  large  parabolic  mirrors  face 
each  other,  as  shown  in  figure  454,  a  watch  at  the  principal  focus  of  one 

mirror  can  be  distinctly  heard  across 
the  room  by  holding  an  ear  trumpet 
at  the  focus  of  the  other  mirror. 

In  buildings  with  arched  ceil- 
ings such  as  the  dome  at  the  Cap- 
itol at  Washington  it  is  possible  to 
hear  a  whisper  at  a  very  distant 
place  in  the  room,  because  the 
sound  is  reflected  from  the  ceiling 
and  concentrated  at  the  ear  of 
the  listener. 

399.  Sound  in  rooms.  Some  halls  and  auditoriums  are  very 
unsatisfactory  because  it  is  almost  impossible  to  hear  well  in 
them.  It  is  therefore  important  to  be  able  both  to  correct 
acoustical  defects  in  existing  auditoriums  and  to  avoid  them 
in  designing  new  ones. 

Sometimes  hearing  is  easy  for  those  in  some  parts  of  a  room  and 
hard  for  those  in  other  parts.  This  sort  of  trouble  is  usually  due  to 
one  or  more  reflections  of  the  speaker's  voice  from  particular  parts 
of  the  walls  or  ceiling,  which  produce,  either  echoes  following  so 
closely  after  the  direct  sound  as  to  confuse  hearers,  or  "dead  spots," 
where  a  reflected  wave  "  interferes  "  (section  414)  with  the  direct 
wave.  Such  cases  are  studied  by  actually  photographing  waves  of 
sound  as  they  pass  through  a  small  cross-sectional  model  of  the 


Fig.   454.     Ticking   of  a   watch   re- 
flected by  mirrors. 


SOUND  IN  ROOMS 


441 


auditorium  in  question  (Fig.  455).  The  remedy  for  a  bad  case  is 
to  put  sound-absorbing  material,  such  as  heavy  tapestries  or  hair 
felt,  on  the  surfaces  from  which  the  objectionable  reflections  come. 

Another  kind  of  trouble  is  due  to  what  is  known  as  reverberation. 
When  a  steady  musical  note  or  vowel  tone  is  sounded  in  a  room,  the 
sound  waves  pouring  out  are  irregularly  reflected  back  and  forth  from 
the  walls,  floor,  and  ceiling  until  the  whole  room  is  uniformly  filled 
with  sound.  This  sound  is  continually  dying  out,  because  each  re- 
flection of  each  wave  is  accompanied  by  more  or  less  absorption  of 
the  sound  energy.  Thus  an  open  window  acts  as  if  it  absorbed  all  of 
the  sound  that  reaches  it,  because  it  lets  all  through  and  reflects  none. 


455- 


Vertical  cross  section  of  a  model  of  a  theater,  showing  a  sound  wave 
moving  toward  the  left. 


In  the  meantime,  fresh  energy  is  being  poured  into  the  room  from  the 
source  of  the  sound,  and  the  general  loudness  very  quickly  increases 
to  a  point  where  all  the  absorption  just  equals  the  flow  from  the  source. 
If  now  the  source  is  suddenly  stopped,  the  sound  already  in  the  room 
begins  to  die  away,  but  remains  audible  for  an  appreciable  time,  some- 
times three  or  four  seconds.  The  duration  of  audibility  after  the 
source  has  stopped  is  used  as  a  measure  of  the  reverberation  of  the 
room.  If  the  reverberation  is  too  small,  a  room  seems  dead  and  un- 
inspiring. If,  on  the  other  hand,  the  reverberation  is  too  great,  three 
or  four  of  the  speaker's  words  may  still  be  ringing  in  our  ears  while 
a  fifth  is  being  spoken,  and  there  is  confusion  and  unintelligibility. 
Most  cathedrals  and  many  stone  churches  have  this  fault,  and  it  has 
led  to  the  custom  of  intoning  the  service,  that  is,  singing  it  all  on  one 
note,  so  that  all  the  words  that  are  being  heard  at  any  one  instant  may 
sound  well  together. 


442  SOUND 

Careful  experiments  by  Sabine  at  Harvard  University  a  few  years  ago 
showed  that  a  room  must  have  a  reverberation  of  almost  exactly  one 
second  to  be  good  for  orchestral  music.  He  also  showed,  not  only 
how  to  correct  excessive  reverberation  by  putting  felt  on  the  walls  or 
ceiling,  or  by  using  sound-absorbing  furniture,  hangings,  statuary,  or 
plants,  but  also  how  to  design  new  auditoriums  so  that  they  shall  have 
just  the  right  reverberation,  by  choosing  proper  materials  for  the  walls 
and  ceiling.  He  even  made  acoustically  good  stone  churches  possible  by 
finding  a  special  kind  of  artificial  stone  or  tile  that  absorbs  many  times 
as  much  sound  as  ordinary  stone. 

400.  Musical  sounds  and  noises.     We  all  recognize  some 
sounds,  such  as  the  slamming  of  a  door  or,  the  rumbling  of  a 
wagon  over  cobblestones,  as  noises;    while  we  recognize  the 
sounds  from  a  piano  wire  or  an  organ  pipe  as  musical  sounds 
or  tones.     The  difference  between  these  kinds  of  sounds  can 

be   best  expressed  by 

A  ^v^7^^  the    curves    in    figure 

456,   where   A   is   the 
curve  of  a  noise  and  B 

Fig.  456.     Curves  to  represent  (A)  noise  and  (B)    the  curve  of  a  musical 

note. 

It  will  be  seen  from  these  curves  that  a  noise  makes  a  very 
irregular  and  haphazard  curve,  while  a  musical  note  makes 
a  uniform  and  regular  curve.  The  latter  produces  an  agree- 
able sensation  on  the  ear,  while  the  former  makes  a  disagree- 
able sensation. 

401.  Three  characteristics  of  a  musical  tone.     A  musical 
sound  or  tone  has  intensity  or  loudness,  pitch,  and   quality 
or  timbre ;    and  each  of  these  characteristics  depends  upon 
some  physical  property   of   the   sound   wave.     The   intensity 
depends  on  the  amplitude  of  the  vibration,  the  pitch  on  the  fre- 
quency of  the  waves,  and  the  quality  on  the  vibration  form. 

402.  Intensity.     We  have  already  seen  that  in  general  the 
intensity  of  sound  diminishes  as  the  distance  of  the  ear  from 
the  source  of  the  sound  increases,  and  also  as  the  density  of  the 
air  diminishes.     The  intensity  of  a  musical  sound  for  a  given 


PITCH 


443 


ear  and  at  a  given  distance  depends  on  the  amplitude  of  vibration 
of  the  waves.  Thus,  a  piano  string  or  a  tuning  fork  gives  a 
louder  sound  when  struck  hard  than  when  struck  gently. 

403.  Pitch.     When  we  speak  of  a  musical  note  as  high  or 
low,  we  refer  to  its  pitch.     When  we  strike  the  keys  of  a  piano 
in  succession,  beginning  at  one  end  of  the  keyboard,  we  recog- 
nize the  difference  in  the  tones  produced  as  a   difference  in 
pitch.     By  holding  a  card  against  the  teeth 

of  a  rapidly  revolving  wheel,  we  can  show 
that  the  pitch  of  the  note  produced  depends 
on  the  number  of  vibrations  per  second; 
that  is,  upon  the  frequency  of  the  vibrations 

We  can  show  this  very  clearly  by  means  of  a 
siren.  This  is  a  metal  disk  (Fig.  457)  with  holes 
equally  spaced  around  the  edge,  which  can  be 
rotated  by  some  sort  of  whirling  apparatus.  If 
a,  current  of  air  is  directed  through  a  tube 
against  the  outer  row  of  holes,  the  regular  suc- 
cession of  puffs  produces  a  musical  tone.  As 
we  increase  the  velocity  of  the  wheel,  the  tone 
becomes  higher;  that  is,  its  pitch  is  raised. 

When  we  place  the  nozzle  of  the  air  current 
opposite  the  row  with  half  the  number  of  holes, 
we  find  that  the  note  is  lower,  and  when  we 

place  the  nozzle  opposite  the  row  of  irregularly  spaced  holes,  we  have 
a  noise. 

One  way  to  measure  the  frequency  of  vibration  of  a  musical  tone  is 
by  means  of  such  a  rotating  disk.  Suppose  the  disk,  h&s  48  holes, 
and  is  attached  to  a  motor  making  1800  revolutions  per  minute. 
Since  the  disk  makes  30  revolutions  per  second,  there  are  30  X  48  = 
1440  puffs  per  second.  The  frequency  of  the  tone  emitted  would 
be  1440  vibrations  per  second.  This  would  be  a  rather  shrill  note. 
A  standard  A  tuning  fork  makes  only  435  vibrations  per  second. 

404.  Limits  of  audibility.     The  lowest  tone  which  the  human 
ear  can  recognize  as  a  musical  tone  has  a  frequency  of  about 
16  vibrations  per  second.     If  the  sound  has  a  frequency  above 
a   certain  number,   the   ear   does   not   hear   it    at    all.     This 
upper  limit  of    audibility  varies  with  different   people  from 


Fig.  457.  The  pitch 
varies  with  the 
speed. 


444 


SOUND 


20,000  to  40,000  vibrations  per  second.  One  of  the  evidences 
of  the  impairment  of  hearing  with  advancing  age  is  the  increasing 
inability  to  hear  sounds  of  high  pitch. 

405.  Quality,  or  timbre.  The  third  characteristic  of  a 
musical  note  is  its  quality.  It  is  quality  which  enables  us  to 
distinguish  between  notes  of  the  same  pitch  and  intensity 
when  produced  by  different  instruments  or  sung  by  different 
voices.  Even  the  same  kind  of  instrument  may  produce  notes 
of  different  quality.  For  example,  it  is  the  quality  of  the  tones 
produced  by  two  violins  which  makes  the  great  difference  in 

their  value.  We  recognize 
the  voice  of  a  friend  over 
the  telephone  by  its  quality. 
Helmholtz  (Fig.  458)  first 
discovered  the  cause  of 
these  subtle  differences  in 
musical  tones  which  are 
called  quality.  In  this  in- 
vestigation he  made  use  of 
resonators  which  vibrated 
in  sympathy  with  the  tones 
to  be  studied. 

406.  Sympathetic  vibra- 
tions. Everyone  has  learned 
by  experience  how  easy  it 
is  to  set  a  swing  vibrating 

by    a     succession    of    gentle 

P^hes  applied  at  just  the 
and  light.  right  time,  so  that  each 

push  helps  rather  than  hin- 

ders the  swinging.  Mere  random  pushes,  on  the  other  hand, 
accomplish  very  little.  In  much  the  same  way,  sound  waves 
or  other  slight  impulses  may  set  up  strong  vibrations  in  a  body 
if  they  are  timed  to  correspond  exactly  to  its  natural  frequency 
of  vibration.  This  is  called  sympathetic  vibration. 


Fig.  458.     Hermann  von  Helmholtz  (1821- 


••• 


RESONATORS 


445 


If 


This  can  be  strikingly  shown  by  holding  down  the  loud  pedal  of  a 
piano,  so  that  -the  dampers  are  lifted  from  the  strings,  and  singing  a 
clear,  strong  tone  into  the  instrument.  After  the  voice  is  silent,  the 
sound  is  returned  by  the  strings  with  startling  fidelity. 

Another  way  to  illustrate  sympathetic  vibrations  is  to  put  two 
mounted  tuning  forks  of  the  same  pitch  several  feet  apart  (Fig.  459). 
If  we  strike  one  fork  vigorously  with  a  soft  mallet,  and  then  quickly 
stop  it  with  the  hand,  the  other  will  be  heard  even  in  a  large  room.  It 
has  been  set  in  motion  by  the  sound  waves  from  the  first  fork, 
we  change  the  pitch  of  one  fork  by 
placing  a  slider  on  one  prong,  the 
•forks  will  be  thrown  slightly  out  of 
unison  and  will  no  longer  respond 
to  each  other. 

From    this     experiment    it    is     Fig    459-     Sympathetic  vibration  of 
•  j  ,  i  •         <•     i  forks  ef  the  same  pitch. 

evident   that   two  tuning  forks 

must  vibrate  at  exactly  the  same  rate  to  vibrate  in  sympathy. 
Certain  articles  of  furniture  and  of  glassware  have  definite 
rates  of  vibration  of  their  own,  and  are  set  vibrating  sympathet- 
ically when  their  particular  note  is  sounded.  It  is  the  cumula- 
tive effect  of  feeble  impulses  repeated  many  times  at  regular 
intervals  which  sets  up  this  sympathetic  vibration. 
407.  Resonators.  The  sound  waves  started 
by  a  vibrating  body  will  cause  another  body  near 
it  to  vibrate,  provided  the  two  have  the  same 
?  rate  of  vibration.  Such  bodies  are  in  resonance. 

In  the  last  experiment  each  tuning  fork  stood  on  a 
wooden  box  open  at  one  end  and  so  constructed 
that  the  air  column  within  the  box  had  the 
same  rate  of  vibration  as  the  fork  itself.  Such 
an  air  column  is  called  a  resonator.  It  was  the 
resonator  rather  than  the  fork  itself  that  picked 
up  the  vibrations. 

To  show  resonance,  we  may  raise  and  lower  the 
tube  A  (Fig.  460)  in  the  jar  of  water  B,  and  at  the 
soundTby  "an  same  time  hold  a  vibrating  tuning  fork  over  the 
air  column.  tube.  We  shall  find  a  position  where  the  sound  of 


446  SOUND 

the  fork  is  reenforced   by  the  sound   of  the  air   column  and  seems 
loudest. 

This  reenf  orcement  or  intensification  of  sound  by  a  resonator 
is  due  to  the  unison  of  direct  and  reflected  waves.  For  example, 
it  can  be  shown  that  the  length  of  air  column  used  in  the  experi- 
ment is  one  quarter  of  a  wave  length.  This  will  be  readily  under- 
stood from  the  diagram  (Fig.  461),  where  ac  is  one  prong  of  a  fork 
vibrating  over  an  air  column  in  resonance. 
—  When  the  prong  moves  down  past  its  cen- 
J~  tral  position,  it  causes  a  condensation  in 
1  the  column  of  air,  which  goes  to  the  bot- 
tom and  gets  back  just  as  the  fork  is 
moving  up  past  its  central  position.  This 
g  reenf  orces  the  vibration  of  the  fork.  Since 
the  sound  traveled  twice  the  length  of  the 
air  column  in  the  time  of  half  a  vibration 
of  the  fork,  it  traveled  the  length  of  the 
air  column  in  the  time  of  a  quarter  vibra- 


Fig.  461.    The  cause  of   tion.     So  the  vibrating  air  column   is   a 
quarter   of  a  wave   length.     Further   ex- 
periments would  show  that  a  resonance    column  may  be  3, 
5,  7,  or  any  odd  number  of  quarter  wave  lengths. 

408.  Forced  vibrations.  When  a  tuning  fork  is  struck,  we  must 
hold  it  close  to  the  ear  to  hear  the  sound  ;  but  if  we  place  its  base  firmly 
against  the  table  top,  the  sound  is  greatly  intensified.  If  we  repeat 
the  experiment  with  another  fork  of  a  different  pitch,  we  find  its  sound 
is  also  reenforced.  Evidently  the  table  intensifies  the  sound  of  any 
fork,  while  an  air  column  would  intensify  only  a  single  note. 

The  vibrations  of  the  fork  are  carried  through  its  base  to 
the  table  top  and  force  the  latter  to  vibrate  with  the  same  fre- 
quency. The  large  surface  of  the  table  top  sets  a  large  quantity 
of  air  in  vibration  and  so  sends  a  wave  of  great  intensity  to  the 
ear.  Sounding  boards  in  pianos  and  other  stringed  instruments 
act  in  much  the  same  way  as  the  table  top  in  this  experiment. 
Such  vibrations  are  called  forced  because  they  can  be  produced 
by  fork  or  string,  no  matter  what  its  pitch. 


OVERTONES 


447 


C.  Second  Overtone 

Fig.  462.  A  wire  emitting  its  funda- 
mental and  its  first  and  second 
overtones. 


409.  Fundamentals   and   overtones.     When   a    piano    wire 
vibrates  as  a  whole,  it  gives  out  what  is  called  its  fundamental 
note.     This  fundamental  is  the  lowest  note  which  it  can  give 
out.     Its  pitch  depends  on  the  length,  tension,  size,  and  ma- 
terial of  the  wire.     When  a  wire  is  vibrating  as  a  whole,  it  may 
at  the  same   time   be   vibrating 

in   segments ;    that   is,    as   if   it 

were    divided     in    the    middle. 

Such  a  secondary  vibration  gives 

•an  overtone  which  has  twice  the 

frequency   of    the    fundamental 

and  is  an  octave  higher.     It  is 

called  kthe  first  overtone.     In  a 

similar  way,  a  string  may  vibrate 

as  a   whole   and,  at   the    same 

time,  as  if  divided  into  thirds; 

in  this  case  it  gives  its  fundamental  and  its  second  overtone 

(Fig.  462) .   Higher  overtones,  or  "  harmonics,"  are  also  possible. 

410.  Helmholtz's  experiment.     Helmholtz  proved  that  the 
quality  of  a  tone  is  determined  simply  by  the  number  and  prominence 

of  the  overtones  which  are  blended  with 
the  fundamental.  To  prove  this,  he  con- 
structed a  large  number  of  spherical 
resonators  (Fig.  463),  each  having  a  large 
opening  A,  and  also  a  small  one  B  adapted 
to  the  ear.  A  resonator  of  this  form  is 
especially  useful  because  it  responds  easily 
to  vibrations  of  one  pitch  only  and  so  can 
be  used  to  analyze  sounds.  By  holding  each  of  these  resonators 
in  succession  to  his  ear,  he  was  able  to  pick  out  the  constituents 
of  any  musical  note  which  was  being  sounded,  and  to  judge  of 
their  relative  intensities.  Then  he  reversed  the  process  and 
combined  these  constituent  overtones,  reproducing  the  original 
tone.  He  thus  succeeded  in  imitating  the  qualities  of  different 
musical  instruments,  and  even  of  various  vowels. 


Fig.   463.     Helmholtz's 
resonator. 


448 


SOUND 


411.  Koenig's  manometric  flames.  Another  method  of 
showing  that  the  quality  of  any  note  depends  on  the  form  of 
the  wave  was  devised  by  a  Frenchman,  Koenig.  This  method, 
called  manometric  flames,  has  the  advantage  of  making  the 
phenomenon  visible. 

The  apparatus  is  shown  in  figure  464.  The  essential  part  is  a  small 
box  divided  into  two  chambers  by  an  elastic  diaphragm,  made  of  very 
thin  sheet  rubber  or  goldbeater's  skin.  The  cavity  on  one  side  is 


Fig.  464.     Analysis  of  sounds  with  manometric  flames. 


connected  with  a  funnel,  while  the  cavity  on  the  other  side  has  two 
openings,  one  for  illuminating  gas  to  enter,  and  the  other  connected 
with  a  fine  jet  where  the  gas  burns  in  a  small  flame.  The  vibra- 
tions of  the  air  on  one  side  of  the  diaphragm  change  the  pressure  of  the 
gas  on  the  other  side,  and  cause  the  flame  to  dance  up  and  down. 

Let  us  set  up  the  apparatus  and  rotate  the  mirror  when  no  note  is 
sounded  before  the  funnel.  There  will  be  no  fluctuations  in  the  flame 
(Fig.  465  a) .  Next  let  an  organ  pipe  be  sounded  in  front  of  the  mouth- 
piece. Then  let  each  of  the  vowels  be  spoken  into  the  funnel  with  the 


PHOTOGRAPHING  SOUND   WAVES 


449 


same  pitch  and  loudness.    The  ribbon  of  flame  seen  in  the  mirror  is 
different  in  each  case  (Fig,  465  6,  c,  and  d). 

Manometric  flames  csin  be  used  to  study  sound  vibrations 
of  such  high  frequency  ihat  they  are  quite  inaudible. 

412.  Photographing  sound  waves.  Professor  Dayton  C. 
Miller  has  invented  a  very  sensitive  instrument  which  photo- 
graphically records  sound 
waves  and  which,  in  a  modi- 
fied form,  can  '  be  used  to 
project  such  waves  on  a 
screen.  This  little  instrument, 
named  the  "  phonodeik/'  is 
very  simple  in  design  but  ex- 
tremely delicate  hi  construc- 
tion. 

The  principle  is  shown  in  fig- 
ure 466 :  h  is  the  receiving  tube ; 
d,  a  diaphragm  of  thin  glass ; 
behind  the  diaphragm  is  a  minute 

steel  spindle  mounted  in  jeweled  bearings,  to  which  is  attached  a  tiny 
mirror  m  •  one  part  of  the  spindle  is  a  small  pulley ;  a  few  silk  fibers  are 

attached  to  the  center  of  the 
diaphragm  and,  after  being 
wrapped  once  around  the 
pulley,  are  fastened  to  a 
spiral  spring ;  a  ray  of  light 
from  the  pinhole  I  is  fo- 
cused by  a  lens  and  re- 
flected by  the  mirror  to  the 
moving  film  /.  As  the  sound  wave  causes  the  diaphragm  to  move 
back  and  forth,  the  mirror  is  rotated  and  the  spot  of  light  traces  a 
record  of  the  sound  wave  on  the  film  as  in  figure  467. 


Fig.  465.    Forms  shown  by  manometric 
flames. 


Fig.  466. 


Diagram  of  the  phonodeik,  used  to 
photograph  sound  waves. 


PROBLEMS 

(Assume  that  the  temperature  is  0°  C.  unless  otherwise  stated.) 

1.    If  two  men  are  1000  feet  and  2500  feet  from  a  foghorn,  how  many 
times  as  loud  does  the  horn  sound  to  one  man  as  to  the  other  ? 


450 


SOUND 


II 

ii-s 

. « 

<->  a 


si 

b  a 


I! 

- 


•3-° 

I! 


•as 


INTERFERENCE  OF  SOUNDS  451 

2.  Six  seconds  elapse  between  the  firing  of  a  gun  and  its  echo  from  a 
cliff.     If  the  temperature  is  15°  C.,  how  far  away  is  the  cliff? 

3.  A  tuning  fork  is  reenforced  when  held  over  an  air  column  6.5 
inches  long.     What  is  the  wave  length? 

4.  A  tuning  fork  whose  normal  frequency  is  435  is  mounted  on  a 
wooden  box,  which  acts  as  a  resonator.     If  we  neglect  the  correction 

for  the  end,  how  long  must  the  box  be  ? 

• 

6.  A  whistle  has  a  resonating  column  of  air  1.5  inches  long.  Find 
the  vibration  frequency  of  its  tone. 

6.  The  parallel  walls  of  a  canon  are  vertical  and  5000  feet  apart. 
A  man  fires  a  gun  in  the  canon  and  hears  two  echoes,  the  second  3 
seconds  after  the  first.     How  far  is  he  from  the  nearer  wall?     Assume 
the  velocity  of  sound  to  be  1100  feet  per  second. 

7.  A  tuning  fork  is  reenforced  when  held  over  an  air  column  10  centi- 
meters long,  and  the  next  position  of  resonance  occurs  when  the  air 
column  is  25  centimeters  long.     Assuming  the  velocity  of  sound  to  be 
345  meters  per  second  at  the  temperature  of  the  room,  compute  the 
frequency  of  the  fork. 

8.  Find  the  frequency  of  a  tuning  fork  which  produces  resonance  in 
a  column  of  air  50  centimeters  long  at  15°  C. 

413.  Interference  of  sounds.  We  have  seen  in  studying 
resonators  that  two  sound  waves  may  unite  so  as  to  reenforce 
each  other.  It  is  also  possible  to  make  two  sound  waves  unite 
so  as  to  interfere  with  or  destroy  each  other.  That  is,  under 
certain  conditions  the  union  of  two  sounds  can  produce  silence. 
This  is  the  cause  of  the  phenomenon  called  beats. 

If  we  place  two  mounted  tuning  forks  of  the  same  pitch  side  by  side, 
and  strike  the  forks  in  succession  with  a  soft  mallet,  we  hear  a  smooth, 
even  tone.  But  if  we  change  the  pitch  of  one  fork  by  attaching  a 
slider  to  one  prong,  and  repeat  the  experiment,  we  hear  a  throbbing, 
or  pulsating,  sound.  The  throbs  are  called  beats.  They  are  due  to  the 
alternate  interference  and  reinforcement  of  the  sound. 

If  two  adjoining  notes  of  a  piano  or  organ  are  struck  at  the  same 
time,  beats  are  heard,  especially  if  the  notes  are  in  the  lower  part  of 
the  scale. 

Beats  are  used  to  tune  two  strings  or  forks  to  the  same  pitch. 
The  forks  are  adjusted  until  no  beats  are  heard. 


452  SOUND 

414.  Explanation  of  beats.  To  show  how  two  sound  waves 
can  combine  to  produce  no  sound,  let  A  in  figure  468  represent 

a  sound     wave,      and     B 

A    \   /   \   /    \    /  \    /\    /    '      another   wave   of   exactly 

v^      Vy      v/      W     W          the  same  period,  but  oppo- 

B     /\   f\   f\    /\   f\    I     sit6  in  phase;  that  is,  just 

^      ^      a  half  wave  length  behind 

c the  first.     If  the  two  im- 

Fig.    468.     Two  waves  of  same  period  but          lges  which  w  r_ 

opposite  phase. 

ate  two  such  waves  were 

applied  to  the  air,  it  would  not  suffer  any  disturbance  at  all 
(curve  C).     This  is  interference  of  sound  waves. 

If  two  waves  of  the  same  period  are  in  phase,  or  in  step,  as  A 
and  B  in  figure  469, 

they      reenf  orce       each     A  -^'^v^^V^^^^/      ^/     x_x 
other    and     produce    a     B    ^-\      ^^     x-\    X"XXX /~ 
sound  of  double  ampli- 
tude, as  shown   by  the     c     A      A     A     A      A     f 
bottom   curve   C.     This        J     \J     \J     \J     \J     \J 

is  reenf  orcement  of  SOUnd    Fig.  469.     Two  waves  in   step  produce  reen- 
Waves.  forcement. 

Finally,  if  two  waves  of  slightly  different  period  (A  and  By 
in  figure  470)  are  superposed,  there  will  be  reenforcement  at 
some  points  and  interference  at  other  points  (curve  C). 

A/VWWWWWWX 

AAAAAAAAA/WWVAAAAA 


Fig.  470.     Curves  to  show  how  beats  are  produced. 


THE  MUSICAL  SCALE  453 

Evidently,  if  the  waves  make  respectively  255  and  256  vibra- 
tions per  second,  there  will  be  one  reinforcement  and  one  inter- 
ference (that  is,  one  beat)  each  second.  In  general,  the  number 
of  beats  per  second  is  equal  to  the  difference  between  the  frequencies 
of  the  waves. 

415.  Discord  and  beats.     Experiments  show  that  discord 
is  simply  a  matter  of  beats.     If  there  are  six  or  more  beats  per 
second,  the  result  is  unpleasant ;  if  there  are  about  thirty,  there 
is  the  worst  possible  discord.     But  when  the  vibration  num- 
bers differ  by  as  much  as  seventy,  as  do  the  notes  C  and  E,  the 
effect  is  harmonious.     If  two  musical  tones  with  strong  over- 
tones are  to  be  harmonious,  it  is  essential  that  there  shall  not 
be  an  unpleasant  number  of  beats  between  any  of  their  over- 
tones.    This  is  the  reason  why  the  bells  of  chimes  are  struck 
in  succession,  not  simultaneously. 

416.  The  musical  scale.     So  far  we  have  been  studying  the 
behavior  of  a  single  train  of  waves  in  the  air,  and  the  propa- 
gation of  a  single  musical  tone ;  now  we  shall  consider  some  of 
the  fundamental  relations  between  musical  tones.     That  is, 
we  shall  seek  a  scientific  basis  of  music. 

When  we  wish  to  compare  two  musical  tones,  we  first  con- 
sider their  pitches  or  frequencies.  Notes  of  the  same  frequency 
are  said  to  be  in  unison.  When  two  notes  have  frequencies  as 
1  to  2,  the  relation,  or  interval,  is  called  an  octave.  Thus,  a 
note  whose  frequency  is  512  is  one  octave  higher  than  another 
whose  frequency  is  256 ;  and  one  whose  frequency  is  128  is 
an  octave  below  the  note  whose  frequency  is  256. 

It  has  been  found  that  the  ear  recognizes  as  harmonious 
only  those  pairs  of  notes  whose  frequencies  are  proportional 
to  any  two  of  the  simple  numbers,  1,  2,  3,  4,  5,  and  6.  It  is 
still  more  remarkable  that  the  ear  of  man  has  for  centuries 
recognized  that  three  notes  are  harmonious  when  their  fre- 
quencies are  as  4  :  5  :  6.  This  combination  is  called  the  major 
triad.  Any  combination  or  rapid  succession  of  tones  not  char- 
acterized by  simple  frequency  ratios  produces  a  discord. 


454 


SOUND 


The  major  scale  is  a  sequence  of  tones  so  related  that  the 
1st,  3d,  and  5th  form  a  major  triad;  also  the  4th,  6th,  and 
8th  (or  octave  of  the  1st) ;  and  also  the  5th,  7th,  and  9th  (or 

octave  of  the  2d). 
This  is  shown  in  the 
following  table,  where 
the  tones  of  the  scale 
are  represented  by 
the  letters  used  in 
musical  notation. 

The  arrangement  of 
the  notes  of  an  octave 
on  the  keyboard  of  a 
piano  is  shown  in  figure  471.  The  white  keys  correspond  to 
the  notes  of  an  octave,  the  black  keys  to  intermediate  notes, 
used  in  forming  other  scales. 

TABLE  OF  RELATIONS  BETWEEN  NOTES  OF  AN  OCTAVE 


i 


International 


m 


rt=i 


Fig.  471.     Notes  of  an  octave  on  a  piano  keyboard. 


c 

(do) 
4 

D 

(re) 

E 

(mi) 

F 

(fa) 

G 

(sol) 

A 

(la) 

B 

(si) 

(do) 

....  . 

d 

(re) 

5 

6 

(8) 

4 

5 

6 

(3) 

4 

5 

6 

1 

* 

1 

1 

3 

-2 

1 

V 

2 

I 

Any  frequency,  or  vibration  number,  may  be  chosen  for  the 
first  note  C  of  the  octave  and  the  series  built  up  as  indicated. 
In  fact,  several  such  pitches  have  been  in  common  use  as  the 
starting  point.  The  so-called  international  pitch  takes  435  vibra- 
tions for  middle  A  (the  second  space  on  the  treble  clef),  and 
this  makes  middle  C  (the  lower  C  on  the  treble  clef)  258.6.  In 
physical  laboratories  C  forks  usually  have  a  frequency  of  256, 
to  make  the  arithmetic  easier. 


VIBRATING  STRINGS  •     455 

MUSICAL  INSTRUMENTS 

417.  Piano.     We  are  all  familiar  with  the  piano,  or  at  least 
we  have  seen  its  keyboard,  which  usually  has  88  keys.     When 
we  open  the  case,  we  find  88  wires  of  various  lengths  and  sizes. 
Each  key  operates  a  felt  hammer,  which  strikes  a  wire  and 
thus  produces  a  note  of  definite  pitch.     We  may  also  notice 
that  the  notes  of  lower  pitch  are  produced  by  long,  large  wires 
and  the  notes  of  higher  pitch  by  short,  thin  wires.     Perhaps 
we  have  watched  a  piano  tuner  loosen  or  tighten  a  wire  by 
'turning  with  a  wrench  a  pin  at  one  end. 

If  we  stretch  a  piece  of  steel  wire  along  the  table  and  set  it 
vibrating,  we  find  its  tone  is  very  weak  compared  with  the  tone 
of  a  piano.  This  is  because  the  piano  has  a  sounding  board 
directly  beneath  the  wires.  The  vibrations  of  the  wires  are 
transmitted  through  the  frame  to  this  large,  thin  board,  causing 
it  to  vibrate  also.  The  board  then  sets  in  vibration  a  larger 
quantity  of  air  than  the  string  alone  could  affect,  and  produces 
a  louder  tone. 

418.  Laws  of  vibrating  strings.     We  may  show  by  means  of  a 
sonometer  (Fig.  472),  which  is  simply  a  metal  wire  stretched  across  a 


Fig.  472.    A  sonometer  used  to  illustrate  the  laws  of  vibrating  strings. 

long  wooden  box,  that  the  pitch,  or  frequency,  of  a  wire  is  raised  by 
tightening  the  wire.  If  the  pull  on  one  wire  is  exactly  four  times  as 
great  as  that  exerted  on  the  other  wire,  then  the  note  of  the  first 
wire  will  be  found  to  be  an  octave  above  that  of  the  second  wire. 
If  we  introduce  a  movable  bridge  or  fret,  the  pitch  is  raised.  The 
shorter  we  make  the  wire,  the  higher  is  the  pitch.  Finally,  we  may  show 
that  a  larger  wire  of  the  same  length  and  under  the  same  tension  gives 
a  lower  note. 


456    • 


SOUND 


Careful  experiments  of  this  sort  have  proved  the  following 
laws : 

(1)  The  vibration  frequency  varies  inversely  as  the  length  of  the 
vibrating  string.     Thus  the  pitch  of  a  wire  under  constant  tension 
is  raised  an  octave  by  putting  the  movable  bridge  in  the  middle. 

(2)  The  vibration  frequency  varies  directly  as  the  square  root 
of  the  tension.     Thus,  if  a  pull  of  4  pounds  on  a  string  gives 
100  vibrations  per  second,  a  pull  of  16  pounds  is  required  to  raise 
the  pitch  an  octave,  or  to  give  200  vibrations  per  second. 

(3)  The  vibration  frequency,  or  pitch,  varies  inversely  as  the 
square  root  of  the  weight  per  unit  length  of  the  string.     This  is 
why  the  wires  of  a  piano  which  give  the  low  notes  are  wound 
with  wire  to  get  the  necessary  weight. 

419.  Other  stringed  instruments.  The  violin,  mandolin,  and 
guitar  have  sets  of  strings  tuned  to.  give  certain  notes,  and 
wooden  bodies  to  reenforce  the  tones  of  the 
strings.  These  instruments  differ  from  the 
piano  in  that  they  have  but  few  strings,  and 
in  that  their  strings  are  set  in  vibration  by 
bowing  or  picking  instead  of  by  striking 
them  with  a  hammer.  Each  string  is  made  to 
give  a  large  number  of  notes  by  pressing  on  it 
at  various  places  and  so  changing  its  length. 
The  particular  place  and  manner  in  which  the 
string  is  plucked  or  bowed  determines  the  over- 
tones and  thus  the  quality  of  the  tone.  In 
this  way  the  violin  may  be  made  to  give  tones 
with  a  wide  range  not  only  of  pitch  but  also  of 
quality. 

420.   Wind  instruments.   The  simplest  wind 
instrument  is  the  organ  pipe.     Sometimes  the 
tube  is  open  at  the  upper  end  and  is  called  an 
open  pipe  (Fig.  473) ;   at  other  times  the  pipe  is  closed  at  the 
upper  end  and  is  called  a  closed  pipe. 


Fig.  473-  Organ 
pipe,  outside 
view  and  cross 
section. 


WIND  INSTRUMENTS  457 

If  we  blow  an  open  pipe,  the  current  of  air  strikes  against  a  sharp 
edge  and  is  set  in  vibration.  The  tube  acts  as  a  resonator.  The  lowest 
note  which  such  a  pipe  gives  out  is  the  one  whose  wave  length  is  twice 
the  length  of  the  pipe.  This  note  is  called  its  fundamental.  If  we 
close  the  end  of  the  tube  with  the  hand,  thus  making  a  closed  pipe,  we 
shall  find  that  the  lowest  note  is  an  octave  lower,  or  one  whose  wave 
length  is  four  times  the  length  of  the  pipe.  This  is  called  the  funda- 
mental note  of  the  closed  pipe. 

In  general,  then,  the  length  of  an  open  pipe  is  one  half  the 
wave  length  of  its  fundamental,  and  the  length  of  a  closed  pipe  is 
one  quarter  of  the  wave  length  of  its  fundamental. 

It  will  be  noticed  that  the  resonance  tube  in  the  experiment 
in  section  407  is  a  closed  pipe  upside  down,  the  tuning-fork 
end  corresponding  to  the  lip  end  of  an  organ  pipe. 

The  flute,  clarinet,  cornet,  and  trombone  are  also  wind  instru- 
ments. In  the  first  two,  the  column  of  air  is  broken  up  by 
means  of  holes.  The  opening  of  a  hole  in  the  tube  is  equiva- 
lent to  cutting  the  tube  off  at  the  hole.  The  length  of  the  air 
column  within  the  cornet  and  certain  other  instruments  can  be 
changed  by  fixed  amounts  by  means  of  pistons  a,  6,  and  c, 


Fig.  474.    The  cornet  and  its  mouthpiece. 

shown  in  figure  474.  In  the  trombone  the  length  of  the  air 
column  can  be  varied  by  sliding  a  portion  of  the  tube  in  and  out. 
It  is  also  possible  to  vary  the  notes  by  blowing  harder  and  so 
getting  overtones. 

In  wind  instruments  of  the  bugle  or  cornet  type,  the  vibra- 
tion of  .the  air  is  caused  by  the  vibrating  lips  of  the  musician. 


458  SOUND 

421.  Vibrating  membranes.     One  example  of  this   sort  of 
musical  instrument  is  the   drum.     Another  is  the  most  won- 
derful musical  instrument  of  all,  the  human  voice.     Its  notes 
are  produced  by  the  vibration  of  a  pair  of  membranes,  one  on 
each  side  of  the  throat,  called  the  vocal  cords,  and  also  by  the 
vibration  of  the  tongue  and  lips.     By  changing  the  muscular 
tension  on  the  vocal  cords,  one  changes  the  pitch  of  the  voice ; 
and  by  changing  the  shape  of   the  mouth,  one  changes  the 
overtones,  and  so  the  quality  of  tone. 

PROBLEMS 

(Assume  that  the  temperature  is  0°  C.,  unless  otherwise  stated.) 

1.  An  open  pipe  is  4  feet  long.     What  wave  length  does  it  give? 

2.  What  is  the  length  of  an  open  pipe  which  gives  a  tone  an  octave 
above  that  in  problem  1  ? 

3.  A  siren  has  50  holes.     How  many  revolutions  per  minute  will 
it  have  to  make  to  produce  a  tone  whose  frequency  is  435? 

4.  A  fork  making  256  vibrations  per  second  is  reenforced  by  a 
tube  of  hydrogen  4  feet  long.     Find  the  velocity  of  sound  in  hydrogen. 

6.    Find  the  number  of  vibrations  of  a  note  three  octaves  below 
a  note  whose  frequency  is  264. 

6.  What  is  the  fourth  overtone  of  a  string  whose  fundamental 
tone  has  a  frequency  of  256  ? 

7.  A  certain  stretched  piano  wire  vibrates  400  times  a  second. 
What  will  be  the  frequency  of  another  wire  of  the  same  material  which 
is  one  half  the  diameter  of  the  first  wire,  and  is  stretched  between  sup- 
ports one  half  as  far  apart  as  the  first,  and  with  one  half  the  tension? 

8.  How  long  would  an  open  organ  pipe  need  to  be  to  give  as  its 
fundamental  tone  the  note  middle  A  (international  pitch)  ? 

9.  How  many  centimeters  long  would  the  closed  pipe  of  a  whistle 
need  to  be  to  give  middle  C  (international  pitch)  ? 

10.  How  many  beats  per  second  will  be  produced  by  sounding  together 
two  open  organ  pipes  20  inches  and  21  inches  long  respectively,  when  the 
temperature  is  20°  C.? 

422.  The   phonograph.     The   phonograph    (Fig.   475)    is   a 
remarkable     machine    for    reproducing    sound.      When   one 


THE  PHONOGRAPH 


459 


speaks  into  the  mouthpiece,  the  waves  set  a  diaphragm  vi- 
brating ;  this  makes  a  fine  metal  or  sapphire  point,  which  can 
move  up  and  down,  cut  a  spiral  groove  of  varying  depth  in 
a  wax  cylinder.  The  bottom  of  this  groove  is  a  wavy  line 


Fig-  475-     Cylinder  form  of  phonograph  and  diaphragm  with  recording  and  re- 
producing points. 

representing  the  condensations  and  rarefactions  of  the  sound 
waves. 

To  reproduce  the  sound,   a  small   round-ended   needle   is 
attached  to  the  diaphragm  and  follows  the  groove  in  the  wax 


Soft' 

rings 
Needle  point  \ 

Fig.  476.     Disk  form  of  phonograph  with  diagram  of  diaphragm  and  needle. 

as  the  cylinder  turns.  The  varying  depth  of  the  groove  moves 
the  needle  up  and  down  and  thus  makes  the  diaphragm  vi- 
brate in  such  a  way  as  to  reproduce  the  original  sounds.  In 


460  SOUND 

the  machine  shown  in  figure  475,  the  sharp  and  the  round- 
ended  points  are  both  mounted  near  the  center  of  the  same 
diaphragm,  as  shown  at  the  right.  The  diaphragm  can  be 
moved  forward  and  back  a  little  so  that  only  one  of  these  points 
touches  the  cylinder  at  any  time. 

In  another  style  of  phonograph  (Fig.  476),  the  wax  is  made 
in   the  form   of  a   disk  instead  of    a    cylinder,     the    needle 

point  vibrates  from  side  to 
side  instead  of  up  and  down, 
and  the  diaphragm  is  verti- 

DiaphraCA    L^ork          ^  cal.     In    still   another   type, 

a  disk  is  used,  but  the  dia- 
phragm is  horizontal  and  is 
Disk  i    -^7~i=^""  vibrated  by  the  up-and  down 

/Diamond  point 

Fig.   477-    Section  of  Edison   diamond    m°tion   °f    a    Diamond    point 
reproducer.  (Fig.  477). 

A    phonograph    does    not 

reproduce  the  consonant  sounds  very  distinctly,  words  being 
chiefly  recognized  by  the  vowel  sounds,  which  come  out  strong 
and  clear.  This  is  because  the  vowel  sounds  are  more  or  less 
clearly  defined  musical  tones,  and  produce  regular  vibrations ; 
but  the  consonant  sounds  are  noises  produced  by  the  mouth 
at  the  beginning  and  end  of  vowel  sounds. 

SUMMARY  OF  PRINCIPLES  IN   CHAPTER  XIX 

Sound,  in  physics,  is  a  vibratory  motion  transmitted  through 

air  or  other  gases,  liquids,  or  solids. 
Velocity  of  sound  in  air  is  about  1100  feet  per  second. 

(Accurately  it  is  1087  ft.  per  sec.  at  0°  C.,  and  it  increases  about 

2  ft.  per  sec.  for  each  degree  C.  rise.) 

Wave  length  =  distance  from  crest  to  crest  (or  from  conden- 
sation to  condensation). 

Frequency  =  number  of  waves  passing  a  given  point   in  one 
second. 


SUMMARY  461 

Velocity  =  frequency  X  wave  length. 

Loudness  of  sound  varies  inversely  as  the  square  of  the  distance. 
Intensity,  or  loudness,  depends  on  amplitude. 
Pitch  (of  musical  tone)  depends  on  frequency. 
Quality  (of  musical  tone)  depends  on  wave  form;  i.e.,  on  num- 
ber and  prominence  of  overtones. 
Pitch  of  a  string  (1)  rises  when  length  is  decreased, 

(2)  rises  when  tension  is  increased, 

(3)  is  higher  for  small,  light  strings. 
Length  of  open  pipe  =  \  wave  length  of  fundamental. 
Length  of  closed  pipe  =  \  wave  length  of  fundamental. 


QUESTIONS 

1.  How  can  the  pitch  of  the  sound  from  a  phonograph  be  raised? 

2.  What  causes  a  difference  in  the  pitch  of  an  organ  pipe  between 
a  hot  day  in  summer  and  a  cold  day  in  winter? 

3.  How  can  a  bugler  produce  notes  of  varying  pitch  on  an  instru- 
ment of  unchanging  length  ? 

4.  Why  is  it  better  to  bow  a  violin  string  near  one  end  rather  than 
in  the  middle  ? 

6.    Is  any  difference  in  the  quality  of  a  violin  tone  noticeable  when 
the  bow  is  moved  nearer  the  finger  board  ?     Why  ? 

6.  A  distant  band  sounds  much  the  same,  except  for  loudness,  as 
a  band  near  by.    What  does  this  indicate  about  the  velocity  of  sounds 
of  different  wave  lengths  ? 

7.  When  an  electric-light  bulb  breaks,  there  is  a  loud  crash.     Why? 

8.  A  man  has  two  open  organ  pipes  which  are  exactly  alike.     He  saws 
off  a  little  from  the  end  of  one.     Explain  what  is  heard  when  they  are 
both  sounded  together. 

9.  There  is  an  old  saying  that   "  if  you  can  count  three  between  a 
flash  of  lightning  and  its  thunderclap,  the  storm  is  not  dangerously 
near."     According  to  this,  how  far  away  must  the  thunder  cloud  be 
for  safety  ? 


462 


SOUND 


478. 


A  common  form  of  automobile 
horn. 


10.  Explain  how  sound  is 
produced  by  the  form  of 
automobile  horn  shown  in 
figure  478. 

PRACTICAL  EXERCISES 

1.  The  mechanism  of  the 
piano  and  the  piano  player. 
Examine  the  wires  and  study 
the  relations  of  their  sizes, 
lengths,  and  tension  to  pitch. 

How  is  a  piano  tuned  ?    Make  diagrams  to  show  the  key  action,  the 

keyboard,   and  octaves.     What   is  the  purpose  of  the  black  keys? 

What  is  the  action  of  the  pedals?     What  is  the  even-tempered  scale? 

Find  out  how  the  air  pressure  in  a  piano  player  controls  the  key  action. 

2.  The  phonograph  in  business.     Find  out  how  the  phonograph 
is  used  in  business  offices  to  save  the  time  of  stenographers.     Discuss 
the  advantages  and  disadvantages  connected  with  its  use. 

3.  The  automobile  muffler.     Why  is  a  muffler  used?     How  is  it-' 
constructed?     Where  is  it  located  on  an  automobile?     How  does  it 
work? 

4.  Musical  pitch.  Look  up  the  history  of  musical  pitch  in  an  encyclo- 
paedia or  in  Helmholtz's  Sensations  of  Tone,  trans,  by  Ellis  (Longmans). 
What  is  meant  by  the  statement  that  certain  people  "  have  absolute 
pitch"?  If  you  know  of  such  a  person,  test  the  accuracy  of  his  pitch 
perception  by  varying  the  speed  of  a  phonograph  and  measuring  its 
revolutions  per  minute. 

6.  Vowel  sounds.  Find  out  from  Miller's  Science  of  Musical  Sounds 
(The  Macmillan  Co.)  how  one  vowel  sound  differs  from  another  even 
when  spoken  or  sung  with  the  same  pitch  and  loudness.  What  bearing 
have  these  differences  on  the  art  of  singing? 


CHAPTER  XX 
ILLUMINATION:  LAMPS  AND   REFLECTORS 

Illumination  —  law  of  inverse  squares  —  standard  lamps 
and  candle  power  —  Bunsen  photometer  —  foot  candles  — 
laws  of  regular  reflection  —  plane  mirrors — concave  mirrors 
—  convex  mirrors  —  graphical  construction  of  image  —  size 
of  image  —  the  mirror  formula. 

423.  Problem  of  illumination.     We  have  to  do  so  much  of 
our  work  and  play  by  lamplight,  that  we  ought  to  know  some- 
thing about  illumination.     Of  course  the  first  essential  is  to 
have    enough    light    to    see    things    distinctly.    Furthermore, 
experience  shows  that  we  may  have  enough  light  and  yet  not 
be  able  to  distinguish  the  position  and  shape  of  objects  well, 
because  the  lamps  are  not  properly  distributed  to  cast  such 
shadows  as  we  are  accustomed  to.     Then  there  is  the  very 
difficult  problem  of  getting  lamplight  which  will  give  colored 
objects  the  same  appearance  as  in  daylight.     Finally,  we  have  to 
protect  our  eyes  from  the  glare  of  modern  powerful  electric  and 
gas  lamps,  which  are  likely  to  give  us  too  much  light  in  spots. 
Besides  these  physical  aspects  of  the  problem  of  illumination, 
there  is  the  economic  question  of  its  cost. 

424.  Light  advances  in  straight  lines.     Everyone  knows  that 
it  is  impossible  to  see  around  a  corner.     This  is  because  light 
under  ordinary  circumstances 

advances  in  straight  lines. 


If  we  set  up  in  a  darkened 
room  a  screen  and  a  lamp,  as 
shown  in  figure  479,  with  an 
opaque  screen  pierced  by  a 
pinhole  in  between,  we  see  an  Fig  4?g  Light  passes  through  pinhole  and 
inverted  image  of  the  fila-  advances  in  straight  lines. 

463 


464 


LAMPS  AND   REFLECTORS 


ment.  This  shows  that  the  light  goes  through  the  hole  in  straight 
lines.  Simple  "  pinhole  "  cameras  are  sometimes  made  on  this  prin- 
ciple. 

The  precise  measurement  of  angles  by  surveyors  depends 
upon  the  fact  that  light  comes  from  the  distant  object  to  the 
observer's  instrument  in  straight  lines. 

Another  consequence  of  this  fact  is  the  formation  of  a  shadow 

when  an  opaque  object 
obstructs  the  passage  of 
light.  The  edge  of  the 
shadow  is,  however,  a 
sharply  defined  transition 

Fig.  480.     Shadow  cast  by  the  earth.  between    light    and    dark, 

only  when  the  source  of  light  is  very  small.  For  example,  the 
shadows  cast  by  an  arc  lamp  are  more  sharply  defined  than 
those  cast  by  a  gas  flame  or  a  Welsbach  mantle.  This  is  also 
true  of  the  shadow  cast  by  the  earth,  as  shown  in  figure  480. 
The  region  A  is  in  the  full  shadow  and  is  called  the  umbra,  while 
in  the  region  BB,  on  either  side,  the  light  grades  off  from  full 
shadow  to  full  illumination.  This  region  is  called  the  pe- 
numbra. When  the  moon  M  happens  to  get  wholly  inside  Ihe 
umbra,  we  have  a  total  eclipse.  When  the  moon  is  partly  in  the 
penumbra,  the  eclipse  is  partial. 

425.  Intensity  of  illumination :  law^f  inverse  s<juar4s.     It 
scarcely  needs  to  be  stated  that  a  book  is  more  brilliantly  illu- 
minated when  it  is  held  near 
a  lamp  than  when  it  is  held 
far  from  the  same  lamp.     In 
other  words,  the  intensity  of 
illumination,     that     is,      the 
amount  of    light  falling  on  a 

Unit    area,   decreases  when  the     Fig.    481.     Illumination   decreases   as 

distance  increases.  the  S(*uare  of  the  distance. 

Let  a  cylinder  of  sheet  metal  which  has  in  it  a  small  pinhole  P 
(Fig,  481)  be  set  up  about  a  lamp,  so  that  the  source  of  light  may  be 


THE  STANDARD  LAMP  465 

considered  a  point.  Then,  one  foot  away,  let  us  put  a  piece  of  card- 
board A  which  has  a  hole  in  it  one  inch  square.  At  a  distance  of  two 
feet  from  the  pinhole,  we  put  a  screen  B.  It  is  evident  that  the  light 
which  passes  through  the  inch  hole  in  A  is  spread  at  B  over  a  2-inch 
square ;  that  is,  over  4  square  inches.  If  we  move  the  screen  B  so 
that  it  is  3  feet  from  P,  the  light  which  passes  through  the  inch  hole 
at  A  is  spread  over  a  3-inch  square;  that  is,  over  9  square  inches. 
The  areas  of  these  squares  increase  as  the  square  of  the  distance.  But 
the  amount  of  light  falling  on  each  total  area  is  the  same.  Therefore 
the  amount  on  each  square  inch  decreases  as  the  square  of  the  distance. 

Intensity  of  illumination  (like  the  intensity  of  sound  and  for 
the  same  reason)  varies  inversely  as  the  square  of  the  distance. 

This  law  assumes  that  the  source 
of  light  is  a  point,  and  that  the 
surface  is  placed  at  right  angles  to 
the  rays  of  light.  In  all  practical 
cases,  however,  the  source  of  light 
is  a  surface,  or  region,  every  point 
of  which  is  giving  light,  and  in  such 
Fig.  482.  illumination  on  an  cases  this  law  is  only  approximately 

inclined  surface   is   less   than  „„  .  .    . 

when  the  surface  is  at  right   true.     When    the    receiving     sur- 
angies.  face  is  inclined  (Fig.  482),  it  does 

not  receive  as  much   light   per  square  inch  as  when  held  at 

right  angles. 

426.  Luminous   intensity   of   a   lamp.     In   computing   the 
amount  of  light  received  on  a  given  area,  we  have  to  consider 
not  only  "the  distance  from  the  source,  but  also  the  luminous 
intensity  of  the  lamp  itself.     A  room,  for  example,  is  much 
more  brilliantly  illuminated  by  a  modern  electric  or  gas  lamp 
than  by  a  kerosene  lamp.     Since  there  are  now  many  different 
forms  of  lamps  on  the  market,  it  is  highly  important  'that  we 
have  some  way  of  measuring  their  luminous  intensities.     To 
do  this  we  must  have  a  standard  lamp  and  some  instrument 
for  the  comparison  of  lamps,  that  is,  a  photometer. 

427.  The  standard  lamp.     Although  many  standard  lamps 
have   been   proposed,   none   is   altogether   satisfactory.     The 


466  LAMPS  AND  REFLECTORS 

oldest  standard  lamp,  which  is  still  used  in  calculation  but 
seldom  in  actual  practice,  is  the  English  standard  candle, 
a  sperm  candle  made  according  to  certain  specifications.  The 
illuminating  power  of  a  horizontal  beam  from  this  candle  is 
called  a  candle  power. 

The  present  value  of  the  candle  power  as  used  in  the  United 
States  is  that  established  by  a  set  of  standard  incandescent 


fc.,^ 

4 


Fig.  483.     Bunsen  photometer. 

lamps  maintained  at  the  Bureau  of  Standards  in  Washington, 
D.  C.  This  unit  of  intensity  is  called  the  international  candle, 
and  has  been  accepted  by  England  and  France.  In  Germany 
the  legal  unit  of  intensity  is  the  Hefner,  which  is  equal  to  0.9 
international  candles. 

In  testing  gas,  sperm  candles  are  still  used  in  routine  work,  although 
the  intensity  of  so-called  standard  candles  may  vary  by  as  much  as 
5  per  cent.  For  more  accurate  work,  the  Harcourt  pentane  lamp  is 
coming  into  use.  This  burns  a  mixture  of  air  and  pentane  vapor  and 
has  an  intensity  of  10  candles. 

The  ordinary  open  gas  flame  consumes  from  5  cubic  feet  of  gas  per 
hour  upward,  and  gives  from  15  to  25  candle  power.  In  Massachusetts 
the  legal  standard  for  gas  is  that  it  shall  give  15  candle  power  in  a 
burner  consuming  5  cubic  feet  an  hour.  Welsbach  lamps  consume 
about  3  cubic  feet  of  gas  per  hour  and  give  50  to  100  candle  power. 

428.  Bunsen  photometer.  This  is  an  instrument  for  com- 
paring the  illuminating  power  of  a  beam  from  a  given  lamp 
with  the  illuminating  power  of  a  horizontal  beam  from  a  stand- 
ard lamp.  This  "grease-spot"  photometer  (Fig.  483)  was  in- 


BUNSEN   PHOTOMETER  467 

vented  by  the  great  German  chemist,  Robert  Bunsen.   It  consists 

essentially  of  a  white  paper  screen  with  a  translucent  spot  in 

the  center,  which  transmits  light  freely.     The  screen  is  placed 

between  the  lamps  to  be  compared,  so 

that  one  side  is  lighted  by  one  lamp  and 

one  by  the  other.     If  the  screen  is  lighted     """" 

more   on  one  side,   that  side  appears 

bright  with  a  dark  spot  in  the  center; 

while   the  other  side  is  darker   with  a 

bright  spot  in  the  center.     If  the  two  Fig.  484.    Bunsen  light  box 

sides  are  equally  illuminated,  the  spot  with  screen. 

disappears,  or  at  least  looks  equally  bright  on  each  side.     The 

grease-spot  screen  is  inclosed  in  a  box  (Fig.  484),  which  is  open 

at  the  ends  A  and  B  toward  the  lamps  to  be  compared.     The 

eye  is  held  in  front  at  E.    Two  mirrors  mi  and  m%  are  placed 

on  either  side  of  the  screen,  as  indicated  in  the  figure,  so  that 

the  two  sides  of  the  screen  can  be  seen  at  the  same  time*. 

429.  Use  of  Bunsen  photometer.  The  photometer  must 
be  used  in  a  dark  room  or  else  in  a  light-tight  box.  The  lamp 
X  to  be  tested  is  placed  at  one  end  of  the  photometer  bar  and  the 
standard  lamp  S  at  the  opposite  end.  The  screen  is  then  moved 
back  and  forth  until  a  position  is  found  where  it  is  equally  illumi- 
nated on  both  sides,  and  the  distances  A  and  B  are  measured. 

It  is  evident  that  if  the  distances  A  and  B  are  equal,  the  candle 
powers  of  the  two  lamps  are  the  same.  If  the  distances  are 
not  equal,  the  lamp  which  is  farther  from  the  screen  has  the  greater 
candle  power.  Furthermore,  since  the  intensity  of  illumination 
decreases  as  the  square  of  the  distance,  the  candle  powers  of 
the  two  lamps  are  directly  proportional  to  the  squares  of  their  dis- 
tances from  the  screen. 

FOR  EXAMPLE,  if  a  lamp  of  candle  power-  X  100  centimeters  from  the 
screen  balances  a  16  candle-power  lamp  80  centimeters  away, 

X        (100)2 

16  =  W 
and  X  =  25  candle  power. 


468 


LAMPS  AND  REFLECTORS 


Fig.     485.      Apparatus    for 
tilting  lamp  to  be  tested. 


430.  Distribution  of  light.  No  lamp  gives  light  uniformly  in  all 
directions.  Thus  in  the  ordinary  kerosene  lamp  the  burner  and  oil 
reservoir  cut  off  the  light  which  would  be  radiated  downward  from 
the  flame ;  and  if  the  flame  is  broad  and  thin,  it  will  give  more  light 
broadside  on  than  edgewise.  Similarly,  an 
incandescent  lamp  gives  different  intensities 
in  different  directions  because  of  the  shape 
of  the  filament. 

Since  an  incandescent  lamp  can  be  easily 
turned  in  any  position  (Fig.  485),  it  is  not 
difficult,  with  the  Bunsen  photometer,  to 
measure  its  candle  power  in  various  posi- 
tions. If  the  candle  power  is  measured  in 
several  directions  in  a  horizontal  plane,  and 
the  results  of  the  tests  averaged,  the  result 
is  called  its  mean  horizontal  candle  power. 
Such  tests  show  that  the  candle  power  in 
various  directions  in  a  horizontal  plane  does 
not  vary  very  much. 
If  the  lamp  to  be  tested  is  tilted  at  different  angles  in  a  vertical 
plane,  the  results  show  that  the  lamp  has  very  low  candle  power  directly 
under  the  tip.  The  results  of  such  tests  may  be  best  shown  graphically 
by  a  diagram  (Fig.  486  A).  In 
this  figure  the  intensity  of  the  light 
in  various  directions  in  a  vertical 
plane  is  indicated  by  the  curve, 
which  varies  in  its  distance  from  the 
center  of  the  concentric  circles  ac- 
cording to  the  intensity  of  the  light. 
Thus,  the  candle  power  directly 
Under  the  tip  of  the  bulb  (0°)  is  a 
little  under  8,  while  horizontally 
(90°)  it  is  16  candles. 

When  it  is  desirable  to  throw  as 
much  light  as  possible  directly  down- 
ward, some  kind  of  reflector  or 
shade  is  used.  Figure  486  B  shows 

the  vertical   distribution    of    light   Fif  •  486.    Photometric  curves 
when  the  bulb  is  fitted  with  a  special 
shade.     From  this  curve  it  will  be 
seen  that  the  horizontal  intensity  is  cut  down  to  6  candles,   while 
the  downward  intensity  runs  over  50  candles.     Such  shades,  made 


30" 


bare  incandescent  lamp  and  (B)  of 
the  same  lamp  with  a  reflector. 


MEASUREMENT  OF  ILLUMINATION 


469 


in  a  great  variety  of  forms  to  give  different  desirable  distributions, 
make  it  possible  to  work  out  scientifically  the  problem  of  lighting  a 
given  room  or  workshop  efficiently. 

431.  Measurement  of  intensity  of  illumination.  We  have 
just  seen  that  the  unit  of  intensity  for  a  source  of  light  is  the 
international  candle.  The  illumination  which  such  a  stand- 
ard candle  throws  upon  a  surface  placed  one  foot  away  and  at 
right  angles  to  the  rays  of  light  is  called  a  foot  candle.  It 
is  the  unit  of  intensity  of  illumination.  Evidently, 


,r  „    x 

Illumination  (foot  candles)  = 


candle  power 


,  ,t.  X 
distance  squared  (ft.) 


Hinged  cove 


Electric 
lamp 


Scree> 


FOR  EXAMPLE,  a  16-candle-power  lamp  would  illuminate  a  surface 
placed  1  foot  from  it  with  an  intensity  of  16  foot  candles.  Again,  if 
the  lamp  were  a  32-candle-power  lamp  and  the  object  were  4  feet  away, 
the  intensity  of  illumination  would  be  ^,  or  2  foot  candles. 

In  these  examples  we  have  assumed  that  there  is  only  one 
source  of  illumination,  and  that  the  surface  is  perpendicular 
to  the  rays  of  light.  In 
practice  this  is  almost 
never  the  case,  so  that 
the  problem  of  computing 
the  intensity  of  illumina- 
tion on  any  given  surface 
is  very  difficult. 

Figure  487  shows  a  very 
simple  instrument  called  a 
foot-candle  meter,  for  meas- 
uring directly  the  intensity 
of  illumination  at  any  place. 
The  most  essential  part  of 
the  instrument  is  a  screen 
with  a  row  of  translucent  spots  which  are  illuminated  from  below  by  a 
tiny  electric  lamp  placed  at  one  end.  In  order  to  make  sure  that  the  lamp 
is  always  at  the  same  intensity,  there  is  an  adjustable  rheostat  con- 
nected in  series  with  the  battery,  and  a  sensitive  voltmeter,  which  regis- 
ters the  voltage  supplied  to  the  lamp.  To  use  the  meter,  one  merely 


Fig- 


A  foot-candle  meter  for  measuring 
illumination  directly. 


470  LAMPS  AND  REFLECTORS 

adjusts  the  rheostat  until  the  voltmeter  indicates  that  the  lamp  is 
getting  the  required  voltage ;  then  one  selects  on  the  screen  the  round 
spot  which  most  nearly  disappears,  that  is,  appears  to  be  of  the  same 
brightness  as  the  white  screen  surface ;  and  finally,  one  reads  off  the 


ILLUMINATION  INSTRUCTIONS  insioe 

FOOT  CANDLES  OB  UUMENS  PER  SQ.  FT. 

!  j  MM,j    | 
10     15   20 


Fig.  488.     The  illuminated  screen  of  a  foot-candle  meter. 

number  of  foot  candles  from  the  point  on  the  scale  which  is  beneath 
this  spot.  For  example,  the  screen  shown  in  figure  488  indicates  10 
foot  candles. 

432.  How  much  illumination  is  needed?  The  amount  of 
illumination  needed  to  furnish  "  good  light  to  see  by  "  varies 
greatly  with  conditions.  For  example,  drafting  rooms,  theater 
stages,  and  stores  require  about  4  foot  candles ;  while  churches, 
residences,  and  public  corridors  may  need  but  1  foot  candle. 
Excessive  light  is  as  undesirable  as  insufficient  light.  Exposed 
light-sources  of  great  brilliancy  (more  than  5  candle  power  per 
square  inch)  constitute  a  common  source  of  eye  trouble.  To 
avoid  this,  electric  bulbs  should  be  frosted  and  distributed  in 
small  units,  or  covered  with  shades  which  diffuse  the  light, 
or  else  concealecl  entirely  from  view.  In  the  latter  case  the 
illumination  is  obtained  by  light  reflected  from  the  ceiling  and 
walls.  This  indirect  system  of  illumination  gives  by  far  the  best 
light,  especially  for  large  rooms  in  public  buildings ;  but  it  costs 
more  than  other  systems,  and  is  to  be  regarded  as  a  luxury. 

PROBLEMS 

1.  If  the  page  of  your  book  is  sufficiently  illuminated  at  a  dis- 
tance of  3  feet  from  an  8-candle-power  lamp,  how  many  candle  power 
will  be  needed  when  you  move  2  feet  farther  away? 

2.  If  a  photographic  print  can  be  made  in  30  seconds  when  held 
3  feet  from  a  light,  how  long  an  exposure  will  be  needed  when  the 
print  is  6  feet  away  ? 


PROBLEMS  471 

3.  A  4-candle-power  lamp  is  120  centimeters  from  a  screen.     How 
far  away  must  a  16-candle-power  lamp  be  to  illuminate  the  screen 
equally  ? 

4.  In  measuring  the  candle  power  of  a  lamp,  a  Hefner  standard 
lamp  (0.90  candle  power)  is  50  centimeters  from  the  grease  spot  of  a 
Bunsen  photometer,  and  the  lamp  to  be  tested  balances  it  when  150 
centimeters  away.     How  many  candle  power  has  the  lamp? 

6.  Two  lamps  give  16  and  32  candle  power  respectively,  and  are 
200  centimeters  apart.  Where  between  the  lamps  may  a  grease-spot 
photometer  screen  be  placed  so  that  its  two  sides  are  equally  illuminated  ? 

6.  What  is  the  illumination  in  foot  candles  on  a  surface  5  feet 
from  an  80-candle-power  lamp  ? 

7.  The  necessary  illumination  for  reading  is  about  2  foot  candles. 
How  far  away  may  a  16-candle-power  lamp  be  placed? 

8.  If  the  lamp  with  the  special  shade  described  in  section  430  is 
to  be  hung  above  a  reading  table,  how  high  should  it  be  placed  ?     (See 
curve  of  distribution,  Fig.  486  B.) 

9.  Compare  the  expense  of  illumination  with  gas  and  electricity. 
A  Welsbach  gas  lamp  burning  5  cubic  feet  of  gas  per  hour  gives  100 
candle  power.     The  gas  costs  90  cents  per  1000  cubic  feet.     A  40-watt 
Mazda  lamp  gives  about  32  candle  power.     Electricity  is  10  cents  per 
kilowatt  hour.     (Find  the  expense  of  each  lamp  per  hour,  and  then 
the  expense  of  1 -candle-power  hour  for  each.) 

10.  A  newspaper  is  sufficiently  illuminated  when  held  2  feet  from  an 
8-candle-power  incandescent  lamp.     How  far  from  a  40-candle-power 
Welsbach  mantle  should  the  paper  be  to  receive  the  same  illumination  ? 

11.  The  electric  lamp  whose  distribution  of  light  is  shown  in  figure 
486  A  is  placed  4  feet  above  and  4  feet  to  one  side  of  a  horizontal  table. 
Find  the  illumination  (foot  candles)  on  the  surface  of  the  table. 

12.  What  is  the  illumination  upon  a  surface  50  yards  from  a  1000- 
candle-power  arc  lamp?     Does  the  illumination  in  this  example  meet 
the  desirable  minimum  of  0.04  foot  candles  for  a  sidewalk? 

PRACTICAL  EXERCISE 

Measurement  of  illumination.  By  means  of  a  foot-candle  meter, 
measure  the  illumination  on  your  study  table  at  home,  on  the  dining- 
^room  table,  and  on  the  living-room  table.  Compare  your  results  with 
the  figures  recommended  by  illuminating  engineers.  (See  Instructions 
accompanying  the  instrument.) 


472  LAMPS  AND  REFLECTORS 

433.  Reflectors,  regular  and  irregular.     We  already  know 
that  we  are  able  to  see  most  objects  about  us  by  the  light  which 
they  reflect  to  our  eyes.     The  surfaces  of  most  objects  are 
rough,    and   so   the   light   striking   them    is    reflected    in    an 

irregular  fashion,  as  shown  in  figure  489. 
This  kind  of  reflection,  or  turning  back,  of  the 
light  we  call  diffused  reflection.  Thus  the 
light  striking  a  piece  of  paper  or  unvarnished 
Fl?efltction  frfnfan  wood  is  scattered.  If,  however,  light  strikes  a 
irregular  surface,  flat  metallic  surf  ace,  carefully  polished  so  that 
it  is  very  smooth,  the  light  enters  the  eye  as  though  coming 
directly  from  a  distant  object,  instead  of  from  the  reflecting 
surface.  This  is  called  regular  reflection,  and  is  illustrated  in 
figure  490,  where  mm  is  the  reflecting  surface,  or  mirror.  The 
line  OP  indicates  the  direction  of  the  light  falling  on  the 
mirror,  and  PE  indicates  the  direction  of  the  reflected  light. 

434.  Law  of  reflection.     When  light  comes  through  a  small 
opening,  the  stream  of  light  is  called  a  beam.     A  very  narrow 
beam  is  called  a  ray.*     When  a  beam  of  light  comes  from  a 
very  distant  source,  such  as  the  sun,  the  rays  of  which  it  is 
composed  are  parallel,  and  so  it  is  called  a  parallel  beam. 

In  figure  490,  let  OP  be  the  direction  of  a  parallel  beam  striking  the 
mirror  mm  obliquely,  and  PE  that  of  the  reflected  beam.  If  a  line  nn, 
called  the  normal,  is  drawn  perpendicular  to  the 
reflecting  surface  at  the  point  P,  the  angle  i  be- 
tween the  normal  and  the  direction  OP  of  the 
incident  beam  is  called  the  angle  of  incidence ; 
and  the  angle  r  between  the  normal  and. the 
direction  of  the  reflected  beam  is  called  the 
angle  of  reflection. 

Careful  experiments  have  shown  that, 

I.  The  incident  ray,  the  normal,  and  the      flection  from  a  smooth 
reflected  ray  lie  in  one  plane.  surface. 

II.  The  angle  of  incidence  is  equal  to  the  angle  of  reflection. 

*  A  more  accurate  definition  of  a  "  ray  "  will  be  given  in  section  453  of  the 
next  chapter. 


PLANE   MIRRORS  473 

435.  Images  in  a  plane  mirror.     We  all  know  that  a  person 
standing  in  front  of  a  plane  mirror  sees  his  own  image  and  that 
of  the  objects  about  him  as  if  they  were  behind  the  mirror.     In 
figure  491  we  see  that  light  coming  from  any  point  A  of  an 
object  is   reflected  by  the  mirror  to 

the  eye  as  if  coming  from  a  point  A' 

back  of  the  mirror.     Similarly,  light 

coming  from   a  group  of  points  (an 

object  A B)   seems  to  come  from  a 

similar    group  of   points    (the   image 

A  'B ')  back  of  the  mirror.     The  group 

of  points  from  which  the  light  appears 

to  come  is  called  the  image  of  the  ob-     Fig.  491.    Image  in  a  plane 

ject.     A   line  A  A'  drawn  from   any 

point  in  the  object  to  its  corresponding  point  in  the  image  is 

perpendicular  to,  and  is  bisected  by,  the  mirror  mm. 

In  general,  an  image  in  a  plane  mirror  is  the  same  size  as  its 
object,  and  as  far  behind  the  mirror  as  the  object  is  in  front. 

Indeed,  such  an  image  is  so  much  like  a  real  object  that 
conjurors  often  make  use  of  the  illusions  due  to  the  invisibility 
of  a  well-polished  mirror.  Since,  however,  the  image  is  reversed 
from  right  to  left,  conjurors  never  allow  a  printed  page  or  clock 
face  to  be  seen  in  a  mirror. 

436.  Uses  of  plane  mirrors.     Good  mirrors  for  household  use  are 
made  of  plate  glass  backed  by  a  thin  coating  of  silver  or  mercury. 
Very  little  of  the  light  is  reflected  from  the  front  surface  of  the  glass ; 
the  rest  is  reflected  from  the  metal  back.     Large  plate-glass  mirrors 
are  sometimes  placed  on  the  walls  of  public  rooms  to  give  an  impres- 
sion of  spaciousness. 

In  scientific  instruments  a  very  small  mirror  is  often  attached  to 
a  rotating  part,  such  as  the  coil  of  a  galvanometer.  Such  a  mirror 
will  turn  a  reflected  beam  of  light  through  twice  the  angle  through 
which  the  mirror  itself  is  turned. 

A  rotating  mirror  MI  is  an  essential  part  of  the  sextant  (Fig.  492) 
which  mariners  use  to  get  the  altitude  of  the  sun.  Attached  to  the 
frame  is  another  plane  mirror  M2,  only  half  of  which  is  silvered ;  the 


474 


LAMPS   AND  REFLECTORS 


Fig.    492.     Sextant   used   to   measure 
angles  in  surveying  and  navigation. 


other  half,  unsilvered,  is  trans- 
parent. There  is  also  a  telescope 
T  attached  to^the  fra^ne  and 
pointing  to  the  half-silvered  mir- 
ror. The  graduations  on  the  circle 
are  made  so  as  to  read  off  directly 
the  degrees  in  the  angle  to  be  meas- 
ured. In  determining  the  angular 
altitude  of  the  sun  above  the  hori- 
zon,, the  mirBor  MI  is  rotated  until 
the  image  of  the  sun  seen  by  double 
reflection  in  Mi  and  M2  coincides 
with  the  image  of  the  horizon  seen 
directly  through  the  unsilvered 


portion  of  the  stationary  mirror  Af2. 

QUESTIONS  AND  PROBLEMS 

1.  Would  a  perfectly  transparent  body  be  visible  ?     Explain. 

2.  Could  you  see  a  perfect  reflecting  surface?     Explain. 

3.  If  a  ray  of  light  strikes  a  plane  mirror  so  that  the  angle  between 
the  ray  and  the  mirror  is  25°,  what  is  the  angle  between  the  incident 
and  reflected  rays  ? 

4.  If  the  mirror  in  problem  3  is  turned  1°,  so  that  the  angle  be- 
tween the  incident  ray  and  the  mirror  becomes  26°,  through  how  many 
degrees  has  the  reflected  ray  been  turned  ? 

5.  A  tree  stands  on  the  edge  of  a  quiet  pond  and  is  inclined  at  an 
angle  of  60°  to  the  surface  of  the  water.     Construct  the  image  of  the 
tree  seen  in  the  water. 

6.  A  woman  5  feet  6  inches  tall  stands  4  feet  in  front  of  a  vertical 
mirror  and  sees  her  entire  image.     What  is  the  shortest  mirror  which  can 
be  used  for  this  purpose  ?     Construct  a  diagram  to  prove  your  answer. 

7.  Two  plane  mirrors  are  placed  at  right  angles  to  each  other  and 
an  object  is  placed  between  them.     How  many  images  will  be  seen? 
Draw  a  diagram  to  show  the  position  of  the  images. 

8.  Explain  with  the  aid  of  a  diagram  the  fact  that  parallel  mirrors 
give  rise  to  an  indefinite  number  of  images  all  on  the  same  line  passing 
through  the  object.     Try  it. 

9.  How  can  you  determine  the  thickness  of  a  plate-glass  mirror 
by  placing  a  pencil  point  upon  it? 

10.   A  room  20  feet  square  has  plane  mirrors  on  opposite  walls.     A 


PRINCIPAL   FOCUS 


475 


493.      Center  of   a 
curved  mirror. 


man  in  the  room  holds  a  lamp  close  to  his  head.  Where  should  he 
stand  so  as  to  be  as  near  as  possible  to  the  twice  reflected  image  of  the 
lamp  in  the  mirrors? 

437.  Curved  mirrors.     A  curved  mirror  is  usually  spheri- 
cal;   that  is,  it  is  a  portion  of  the  surface  of  a  sphere.     If  it 
is  a  portion  of  the  outer  surface,  it  is  f, ^ 

called  a  convex  mirror  ;  if  it  is  a  portion 
of  the  inner  surface,  it  is  called  a  con- 
cave mirror.  The  center  of  the  sphere 
of  which  the  curved  mirror  is  a  portion 
is  called  the  center  of  curvature  (C  in 
Fig.  493).  The  line  CM  connecting  the 
middle  of  the  mirror  M  with  the  center 
of  curvature  C  is  called  the  principal 
axis.  Any  other  straight  line  through  the  center  of  curvature, 
such  as  CS,  is  called  a  secondary  axis.  It  will  be  noticed  that 
any  axis  is  perpendicular  to  the  reflecting  surface. 

438.  Principal  focus.     When  a  beam  of  light  parallel  to  the 
principal  axis  strikes  a  concave  mirror,  the  rays  are  so  reflected 
as  to  pass  through,  or  very  close  to,  a  single  point  (Fig.  494). 

This  point  is  called 
the  principal  focus  of 
the  mirror.  It  may  be 
defined  as  that  point 
where  all  rays  parallel 
to  and  near  the  princi- 
pal axis  of  a  mirror 
meet  after  reflection. 
The  distance  from  the 
principal  focus  to  the 
mirror  is  .called  its  focal 
length  and  is  one  half  its  radius  of  curvature. 

We  may  show  that  the  principal  focus  is  located  half  way  between  the 
mirror  and  its  center  of  curvature.  Suppose  the  ray  QP  in  figure  495, 
parallel  to  the  axis  A  B,  strikes  thejmirror  at  the  point  P  and  is 
reflected  back  in  the  direction  PF,  so  as  to  make  the  angle  of  incidence  i 


Fig.    494- 


Concave  mirror   converges    parallel 
rays. 


476  LAMPS  AND   REFLECTORS 

equal  to  the  angle  of  reflection  r. 
Since  QP  and  AB  are  parallel  lines, 
the  angle  i  is  equal  to  the  angle  a. 
Therefore  the  angle  a  must  be  equal 
to  the  angle  r,  and  CF  =  PF.  But 
when  P  is  near  0,  PF  is  nearly 
equal  to  FO,  which  means  that  F  is 

about    midway   between   C   and   0. 
Fig.   495-    Location  of  principal       It    can    be  ed    that    the        in_ 

focus.  .    ,  i  •  T     • 

cipal  focus,    which  is  very  close  to 

F,  is  exactly  halfway  between  C  and  0. 

All  the  rays  parallel  to  the  principal  axis  of  a  concave  spheri- 
cal mirror  do  not  meet  exactly  at  the  same  point  after  reflection. 
This  failure  of  the  rays  to  converge 
accurately  at  a  point  is  called  spherical 
aberration.  This  imperfection  is  slight 
when  only  a  small  portion  of  a  sphere  is 
used  as  a  mirror.  Spherical  aberration 
in  a  large  mirror  is  shown  in  figure  496, 
where  it  will  be  observed  that  only  the 
central  rays  are  reflected  through  the  Fig.  496.  Aberration  in  a 
focus  F,  while  the  rays  which  strike  spherical  concave  mirror 
the  mirror  near  the  edge  are  reflected  decidedly  to  the  right  of  F. 
It  is  sometimes  necessary,  as  in  the  case  of  a  searchlight,  to 
take  the  divergent  rays  of  an  arc  lamp 
and  reflect  them  all  in  one  direction. 
/  ^~  This  can  be  done  roughly  with  a  concave 

spherical  mirror,  by  putting  the  arc  at 


/  F 

' > the    principal  focus ;  for  then  the  rays 


\  >~  travel  the  same  paths  as_above,  but  in 


\  the  opposite  direction.     To  avoid  spheri- 

^S^— — > — •         cal  aberration,  however,  a  parabolic  mir- 
^**  ror  (Fig.  497)  is  generally  used. 

Fig.  497.    Parabolic  mirror. 

439.  Uses  of  concave  mirrors.  The  oph- 
thalmoscope is  a  concave  mirror  with  a  little  hole  in  it.  With  this 
instrument  a  physician  can  reflect  light  from  a  lamp  into  a  patient's 


CONCAVE  MIRRORS 


477 


Fig.  498.  Reflecting  telescope,  with  a  concave  mirror,  100  inches  in  diameter, 
at  Mount  Wilson  Observatory,  Pasadena,  California.  The  two  large  drums 
at  the  ends  of  the  solid  beam  float  in  mercury.  Notice  the  movable  observing 
platform  in  the  upper  right-hand  corner. 


478 


LAMPS  AND  REFLECTORS 


Fig.  499. 


Convex  mirror  and  virtual 
focus. 


eye,  nose,  or  throat,  and  at  the  same  time  look  through  the  hole  into  the 

cavity  thus  illuminated. 

A  certain  type  of  telescope,  called  a  reflecting  telescope  (Fig.  498), 

consists  of  a  long  tube  with  a  concave  mirror  at  one  end,  which 

forms  an  image  of  a  distant  object. 
The  only  purpose  of  the  tube  is  to 
support  near  its  open  end  an  eye- 
piece or  magnifying  glass  through 
which  the  image  can  be  advanta- 
geously examined. 

In  a  compound  microscope  light 
from  a  window  or  lamp  is  concen- 
trated upon  the  object  to  be  exam- 
ined, by  means  of  a  concave  mirror. 
Concave  mirrors  are  extensively 
used  in  searchlights  and  headlights. 

440.  Convex  mirror.     When  a  beam  of  light  parallel  to  the 
principal  axis  strikes  a  convex  mirror  (Fig.  499),  the  rays  are 
reflected  as  if  they  came  from  a  point  F  which  is  behind  the 
mirror,  and  halfway  between  C,  the  center  of  curvature,  and  the 
mirror.     The  point  F  is  called  a  virtual  focus,  because  the  rays 
do  not  actually  pass  through  it,  but  simply  look  as  if  they 
had  come  from  it.     In  the  case  of  the  concave  mirror  the  rays 
do  actually  pass  through  the  point  F ;  this  is  shown  by  the  fact 
that  a  large  concave  mirror  of  short  focal  length  causes   so 
great  a  concentration  of  the  sun's  radiant  energy  that  paper  and 
wood  may  be  ignited  if  placed  at  F.     Such  a  focus  is  a  real 
focus. 

The  image  of  any  object  in  front  of  a  convex  mirror  appears 
to  be  behind  the  mirr®r  and  seems  to  be  erect  but  smaller. 
For  this  reason  small  convex  mirrors  are  often  fastened  to 
the  windshields  of  automobiles  to  show  the  driver  what  is  com- 
ing from  behind. 

441.  Construction  of  images.     It  is  possible  to  learn  a  great 
deal  about  the  position  and  size  of  images  formed  by  mirrors, 
by  carefully  constructing  diagrams  to  show  the  paths  of  the 
rays  of  light. 


CONSTRUCTION  OF  IMAGES 


479 


Fig.  500. 


Construction  of  image  in  a  con- 
vex mirror. 


Suppose  mn  in  figure  500  is 
a  convex  mirror,  and  AB  an 
object.  Let  us  draw  A.C,  a  ray 
normal  to  the  mirror.  This 
ray  will  be  reflected  directly 
back  on  itself  at  P.  Again  let 
us  draw  A  D  parallel  to  the  prin- 
cipal axis.  This  ray  will  be 
reflected  as  if  it  came  from  F 
(the  focus). _  The  image  point 
of  A  will  be  at  A '  where  these 
two  reflected  rays  cross.  In 
'the  same  way  B'  is  located. 

This  construction  shows 
that  the  image  in  a  convex  mirror  always  seems  to  be  behind 
the  mirror  and  smaller  than  the  object.  It  is  erect  and  nearer 
the  mirror  than  is  the  object.  It  is  always  a  virtual  image. 
Thus  a  person  sees  a  virtual  image  of  his  face  in  a  polished  ball. 
It  is  always  right  side  up  and  of  small  size. 

Suppose  mn  (Fig.  501)  is  a  concave  mirror,  of  which  C  is  the  center 
of  curvature.  Let  AB  be  an  object  which  is  placed  beyond  the  center 
of  curvature.  To  determine  the  position  of  the  image,  let  us  trace 
two  rays  from  A.  If  A P  is  one  such  ray  passing  through  C,  it  will  hit 
the  mirror  perpendicularly  and  be  reflected  directly  back  along  the  line 
PC.  If  the  other  ray  from  A  is  AD,  parallel  to  the  axis,  it  will  be 
reflected  so  as  to  pass  through  the  focus  F.  The  point  A ',  where  they 

intersect    after    reflec- 
\  N^          tion,  is  the  image  of  A. 

In  a  similar  way  the 
image  of  B  is  located  at 
B' ;  so  the  image  of  the 
arrow  AB  will  be  the 
arrow  A 'B'. 


Fig.  501 .    Construction  of  image  in  a  concave  mirror. 


It  will  be  seen  that 
when   the    object   is 


beyond  the  center  of  curvature,  the  image  is  inverted  and  in 
front  of  the  mirror.  Since  the  rays  of  light  from  A  really  do 
pass  through  A',  the  image  is  real. 


480 


LAMPS  AND  REFLECTORS 


442.  Size  of  a  real  im- 
age. Let  us  draw  the  ray 
AO  and  its  reflected  ray 
0 A'  (Fig.  502).  From  the 
law  of  reflection,  the  angle 
of  incidence  i  is  equal  to 
the  angle  of  reflection  r. 
Fig.  502.  To  get  size  of  a  real  image.  Therefore,  the  right  tri- 
angles AOB  and  A  'OB' 

are  similar,  and  their  corresponding   sides   are  in  proportion. 

That  is, 


A'B' 
A  B 


B'O 
BO 


Dj 
Do 


The  size  of  the  image  is  to  the  size  of  tne  object  as  the  distance 
of  the  image  from  the  mirror  is  to  the  distance  of  the  object  from 
the  mirror. 

443.  Conjugate  foci.     We  have  seen  in  figure  501  that  when 
A  is  the  object  point,  the  image  point  is  at  A'.    But  if  A'  is 
the  object  point,  the  image  point  is  at  A  ;   for  the  rays  will 
travel  the  same  paths  in  the  other  direction.     For  example,  if 
a  lamp  were  put  at  A  B,  an  inverted  smaller  image  would  be 
formed  on  a  screen  placed  at 

A'B' ;  also  if  the  lamp  were 
put  at  A  'Bf,  the  image  would 
be  inverted,  larger,  and  lo- 
cated at  AB  (Fig.  503). 

Two    points,    so    situated 
that  light  from  one  is  con- 
centrated at  the  other,   are    pig.  503 
called    conjugate    foci.     For 
example,  B  and  B'  in  figure  501  are   wo  such  points  and  there- 
fore are  conjugate  foci. 

444.  Virtual  image  in  a  concave  mirror.     We  have  just 
seen  that  when  the  object  is  beyond  the  center  of  curvature, 


Conjugate  foci  of  a  concave 
mirror. 


SIZE  OF  A    VIRTUAL  IMAGE 


481 


the  image  is  between  the  principal  focus  F  and  the  center  of 
curvature  C.     Also  when  the  object  is  between  F  and  C,  the 
image  is  beyond  C.     In  both 
cases,  the  image  is  real ;  the  im- 
age is  always  real  when  the  object 
is  outside  the  principal  focus  F. 

When,  however,  the  object  is 
placed  inside  the  principal 
focus,  that  is,  between  F  and 
the  mirror  as  shown  in  figure 
504,  the  image  is  behind  the 
mirror,  erect,  enlarged,  and 
virtual. 


Fig.  504.     Construction  of  virtual 
image  in  concave  mirror. 


A' 


To  show  this  we  may,  as  before,  trace  two  rays  from  the  point  A, 
one  parallel  to  the  axis,  which  is  reflected  through  F,  and  the  other 
perpendicular  to  the  mirror,  which  is  re- 
flected back  on  itself  through  C.  They 
will  diverge  after  reflection  and  must  be  pro- 
duced backward  to  find  the  point  of  inter- 
section A '.  The  image  A '  is  a  virtual  image, 
because  the  light  from  A  does  not  actually 
pass  through  A'. 

445.  Size  of  a  virtual  image.  Since 
every  ray  from  A  (Fig.  505)  is  reflected  so 
as  to  seem  to  come  from  A',  the  ray  from 
A  to  M,  the  middle  of  the  mirror,  will  be 


505.    To  get  size  of  a 
virtual  image. 


reflected  in  the  direction  A'MC.    Since  the  angles  of  incidence  and 
reflection  are  equal, 

angle  AMB  =  angle  BMC. 

But  A' MB'  and  BMC  are  vertical  angles  and  equal.     So 

angle  AMB  =  angle  A' MB'. 

Therefore  the  right   triangles   A  MB  and    A  'MB'  are  similar,   and 

A'B'       B'M 


~AB 


BM 


So  in  this  case,  as  before,  the  size  of  the  image  is  to  the  size  of  the  object 
as  the  image  distance  is  to  the  object  distance. 


482  LAMPS  AND  REFLECTORS 

446.    The  mirror  formula.     Let  O  in  figure  506  be  an  object  on  the 
axis,  and  OM  any  ray  from  O  meeting  the  mirror  at  M.     Draw  the 

radius  CM  and  construct  the  reflected 
ray  MI,  making  angle  CMC  =  angle 
CM  I.  Then  7  is  the  image  of  0.  Since 
CM  is  the  bisector  of  the  angle  OMI,  it 
follows  that 

1N 

OM       OC  H 

TM  =  ~Tc'  ^ 

Fig.  506.     Location  of  real  images 

in  concave  mirror.  Let    IN  =  ^    and   Qff  =  ^       wheQ 

the  aperture,   that  is,  the  angle  MON,  is  small,  we  have  the  approxi- 
mate relations 

OM  =  ON  =  Do,  and  IM  =  IN  =  Dt. 
Now,  since  FN  =  /, 

OC  =  ON  -  CN  =  Do  -  2/ 
1C  =  CN  -  IN  =  2f  -  Dl. 

Substituting  these  values  in  the  proportion  (1),  we  have 

Do  _  Dp  -2f 
Dl        2f  -  Dl 
which  reduces  to  DJ  +  D0f  =  Z)0£>i. 

Dividing  by  D0  X  Di  X  /,  we  have 

JL,  i=_L 
D0^~Dl        f 
where 

D0  =  distance  of  object  from  mirror, 
DI  =  distance  of  image  from  mirror, 

/  =  focal  length  of  mirror. 
Stated  in  words 

x 


Object  distance        image  distance       focal  length 
This  equation  gives  us  a  useful  relation  between  the  distance 

of  the  object  from  the  mirror,  the  distance  of  the  image,  and 

the  focal  length.     If  any  two  of  these  three  quantities  are 

known,  the  third  can  be  calculated. 

It  can  be  proved  that  this  equation  holds  as  it  stands  for 

all  cases  of  images  either  real  or  virtual,  formed  in  a  concave 


PROBLEMS  483 

mirror.  If  the  value  of  Dl  comes  out  negative  for  certain 
values  of  D0  and  /,  as  it  will  when  D0  is  less  than  /,  the  mean- 
ing is  that  the  image  is  behind  the  mirror ;  that  is,  the  image 
is  virtual.  It  can  be  shown  that  it  holds  also  for  convex  mirrors, 
if  the  focal  length  /  of  a  convex  mirror  is  regarded  as  negative. 
In  the  next  chapter  we  shall  see  that  this  same  equation 
holds  for  lenses. 

PROBLEMS 

1.  An  object  is  placed  15  inches  from  a  concave  mirror  whose  radius 
.of  curvature  is  12  inches.     How  far  from  the  mirror  is  the  image  ?     Is 
it  real  or  virtual,  erect  or  inverted? 

2.  If  the  object  in  problem  1  is  3  inches  long,  how  long  is  the 
image  ? 

3.  An  object  is  placed  12  inches  from  a  concave  mirror  whose 
focal  length  is  8  inches.    How  far  from  the  mirror  is  the  image?    Is  it 
real  or  virtual,  erect  or  inverted  ? 

4.  If  the  object  in  problem  3  is  2  inches  long,  how  long  is  the 
image  ? 

5.  An  arrow  1  inch  long  is  placed  4  inches  from  a  concave  mirror 
whose  radius  of  curvature  is  12  inches.     Find  the  position,  length,  and 
nature  of  the  image. 

6.  If  the  image  of  a  candle  flame,  placed  10  inches  from  a  concave 
mirror,  is  formed  distinctly  on  a  screen  30  inches  from  the  mirror,  what 
is  the  radius  of  curvature? 

7.  How  far  from  a  concave  mirror  whose  focal  length  is   2  feet 
must  a  man  stand  to  see  an  erect  image  of  his  face  twice  its  natural 
size? 

8.  Where  must  an  object  be  placed  to  form,  in  a  concave  mirror 
whose  focal  length  is  10  inches,  a  real  image  one  half  as  long  as  the 
object  ? 

9.  The  radius  of  curvature  of  a  convex  spherical  mirror  is  20 
inches.    Find  the  position  of  the  image  of  an  object  5  feet  from  the 
mirror. 

10.  Given  a  concave  mirror  whose  radius  of  curvature  is  90  centi- 
meters ;  find  two  positions  where  an  object  can  be  placed  and  produce 
an  image  which  is  three  times  as  long  as  the  object. 


484  LAMPS  AND  REFLECTORS 

SUMMARY  OF  PRINCIPLES   IN   CHAPTER   XX 

Intensity  of  illumination  varies  inversely  as  square  of  distance. 
Candle  powers  of  lamps  giving  equal  illumination  are  directly 

proportional  to  the  squares  of  their  distances  from  screen. 

(That  is,  lamp  farther  away  is  more  powerful.) 
Unit  intensity  of  illumination,  or  foot  candle,  is  illumination  due 

to  a  one-candle-power  lamp  one  foot  away. 

.  .  candle  power 

Illumination  (foot  candles)  =  — ,  ,.  .,• 

distance  squared  (ft.)2 

In  regular  reflection : 

I.   Incident,  normal,  and  reflected  rays  all  in  one  plane. 
II.    Angle  of  reflection  =  angle  of  incidence. 
Plane  mirror :  Image  always  behind  mirror,  erect,  virtual,  same 
size  as  object,  and  at  same  distance  from  mirror  as  object. 
Principal  focus  of  curved  mirror  (either  concave  or  convex) ; 
Defined  as  convergence  point  for  rays  parallel  to  axis  of  mirror, 
Located  halfway  between  mirror  and  center  of  curvature. 
Concave  mirror : 

If  object  is  outside  focus,  image  is  also  outside  focus,  and 
center  of  curvature  is  between  object  and  image.    Image  is 
inverted  and  real. 
If  object  is  inside  focus,  image  is  behind  mirror,  erect  and 

virtual. 

Convex  mirror :  Image  always  behind  mirror,  erect  and  virtual. 
Mirror  formula  (holds  for  both  concave  and  convex  mirrors) : 

1 1 =  1 

Object  distance       image  distance         focal  length 
Object  distance  is  always  to  be  taken  as  positive. 
Image  distance;  positive  for  real  images  and  negative  for  virtual 
Focal  length;  positive  for  concave  mirrors  and  negative  for  convex. 
Size  rule  (holds  for  both  concave  and  convex  mirrors) : 
Length  of  image  _  image  distance  (from  mirror) 
Length  of  object  ~~  object  distance  (from  mirror) 


QUESTIONS 


485 


QUESTIONS 

1.  What  is  the  difference  between  16  candle  power  and  16  foot 
candles  ? 

2.  How  can  a  Welsbach  gas  lamp  consuming  only  3  cubic  feet  of  gas 
per  hour  give  over  50  candle  power,  when  an  ordinary  gas  jet  using  5  or 
more  cubic  feet  per  hour  gives  only  about  18  candle  power. 

3.  If  light  from  a  very  distant  object,  such  as  the  sun,  falls  on  a 
concave  mirror,  where  is  the  image  formed  ? 

4.  How  does  the  curve  of  a  parabola  differ  from  the  arc  of  a  circle  ? 

5.  How  does  the  action  of  a  parabolic  mirror  differ  from  that  of  a 
•concave  spherical  mirror? 

6.  What  is  the  danger  in  too  great  intensity  of  illumination? 

7.  Explain  how  the  image  of  a  man  standing  in  front  of  a  plane 
mirror  which  is  tilted  so  as  to  make  an  angle  of  45°  with  the  floor 
appears  horizontal. 

8.  A  person-  looking  into  a  mirror  sees  a  very  small  image  of  his 
face  upside  down.     What  kind  of  mirror  is  it  ? 

9.  Show  by  a  diagram  how  a  tailor  arranges  two  mirrors  so  that 
a  customer  can  see  the  back  of  his  coat. 

10.  Describe  the  changes  in  the  position 
and  nature  of  the  image  of  a  luminous  point, 
as  the  point  is  moved  from  a  great  distance 
up  to  a  concave  mirror  along  its  axis. 

PRACTICAL  EXERCISE 
Automobile   headlights.     What   type    of 
electric  lamp  is  legal  for  headlights  in  your 
state?     Determine  the  focus  of  a  headlight 
mirror  (Fig.  507).     By  experiment  find  the 
effect  of  placing  the  lamp  filament  in  front 
of  the  focus.      Construct  a  diagram  to  show  pjg.  S07     Automobile  head- 
the  reason  for  this  effect.  light  with  parabolic  mirror. 


Bulb  Adjusting  Screw^ 
Lamp  Sheli 


CHAPTER   XXI 
LENSES  AND   OPTICAL  INSTRUMENTS 

Refraction  —  law  of  refraction  —  speed  of  light  —  wave 
fronts  —  explanation  of  refraction  —  index  of  refraction  as 
ratio  of  speeds  —  total  reflection  —  prism  —  lenses  —  lens 
equation  —  size  rule  —  defects  of  lenses. 

Camera  —  eye  —  defects  of  eye  —  projecting  lantern  — 
motion  pictures  —  magnifying  glass  —  microscope  —  telescope 
—  erecting  telescope  —  opera  glass  —  prism  binocular. 

447.  Optical  instruments.     The    human    eye    is    the   most 
common  and  at  the  same  time  one  of   the  most  remarkable 
optical   instruments   known.     Human   eyes   are   often   imper- 
fect in  various  ways,  and  have  to  be  "  corrected,"  or  rather, 
aided  in  their  work ;  for  defective  eyes  themselves  are  seldom 
changed   by  spectacles   or  eyeglasses.     These,   too,   we  shall 
study  in  this  chapter.     Even  a  healthy  eye  has  its  limitations, 
and  many  optical  instruments  have  been  devised  to  help  it  to 
see  things  too  far  away  or  too  small  for  ordinary  vision.     And 
finally,  there  are  many  devices,  such  as  cameras,  stereopticons, 
and  motion-picture  machines,  that  enable  us  to  see  things  far 
away  from,  or  long  after,  their  actual  occurrence.     All  these 
devices  for  enabling  us  to  see  better,  farther,  or  at  a  different 
time  are  called  optical  instruments. 

In  all  of  them  we  find  lenses,  and  in  some  of  them  also  prisms. 
To  understand  how  optical  instruments  work,  we  must  first 
study  the  passage  of  light  through  lenses  and  prisms ;  that  is, 
the  refraction  of  light. 

448.  Refraction  in  water.     When  a  stick  stands  obliquely 
in  water,  it  appears  to  be  broken  at  the  surface  of  the  water 

486 


LAW  OF  REFRACTION 


487 


stick  partly  in  water  appears 
broken. 


in  such  a  way  that  the  part  under  water  seems  to  be  bent  up- 
ward (Fig.  508) .  The  bottom  of  a  tank  of  water  always  appears 
to  be  nearer  the  surface  than  it  really  is.  A  fish  appears  to  be 
higher  in  the  water  than 
it  actually  is,  so  that  if 
one  wishes  to  spear  it,  one 
must  aim  under  its  image. 
All  these  phenomena  are 
due  to  the  refraction  of 
the  light  as  it  passes  from 
water  into  air.  We  have  Flg-  5°8 
said  that  light  advances  in 
straight  lines :  but  this  is  only  true  in  a  single  substance.  In 
general,  when  light  goes  from  one  substance  into  another  of  different 
density,  it  is  bent,  or  refracted,  at  the  dividing  surface. 

449.  Law  of  refraction.  To  measure  how  much  a  beam  of 
light  is  bent  in  passing  from  water  into  air,  we  may  perform  the 
following  experiment. 

We  set  a  board  vertically  in  a  jar  of  water  and  fasten  a  wire  (solder) 
with  pins  along  the  board  (Fig.  509).  If  we  fill  the  jar  with  water,  and 
then  look  down  along  the  wire,  we  see  that  the 
part  under  water  appears  to  be  bent  upward. 
If  we  bend  the  part  that  is  out  of  water  until 
the  whole  wire  seems  to  be  straight,  we  have  a 
model  to  show  the  path  of  the  light  in  air  and 
water.  We  may  now  remove  the  board  from 
the  water  and  draw  the  water  line  and  the 
perpendicular  (Fig.  510). 

From  this  experiment  we  see  that  a 
beam  of  light  in  passing  from  water  into  air 
is  bent  away  from  the  perpendicular. 

It  might  also  be  shown  that  a  beam  of  light 
in  passing  from  air  into  water,  in  the  direction 
BO,  is  bent  in  the  direction  OA  (Fig.  510).  That  is,  a  beam  of  light 
in  passing  from  air  into  water  is  bent  toward  the  perpendicular.  In 
this  case  the  line  BO  represents  the  incident  ray  and  the  line  OA  the 
refracted  ray.  The  angle  COB  between  the  incident  ray  and  the 


Fig.  509.  Light  is  bent 
when  leaving  water 
obliquely. 


488 


LENSES  AND  OPTICAL  INSTRUMENTS 


normal  is  called  the  angle  of  incidence,  and  the  angle  AOD  between 
the  refracted  ray  and  the  normal  is  called  the  angle  of  refraction. 

To  show  the  relation  between  the  angles  of  incidence  and 
refraction,  we  lay  off  equal  distances  on  the  incident  and  re- 
fracted rays  (AO  =  BO),  and  draw 
perpendiculars  to  the  normal  (AD 
and  BC).  We  shall  find  that, 
whatever  the  angle  of  incidence, 
the  line  BC  is  always  a  definite 
number  of  times  greater  than  AD. 
For  example,  in  this  case  BC  might 
be.  4  inches,  while  AD  might  be 
3  inches,  and  then  the  ratio  BC/  A  D 

Fig.  510.     Diagram  of  refraction    is  %>  or    1-33*     This  ratio  is  Called 

of  light  passing  from  air  into  the  index  of  refraction.      Experi- 
ments show  that  this  ratio  is  always 

the  same  for^JLlw-game  two  substances,  no  matter  what  the  angle 
of  incidence  may  be. 

This  ratio  may  also  be  expressed  in  terms  of  the  "  sines  "  of  the 
angles  of  incidence  and  refraction.  Sine  is  the  name  used  in 
trigonometry  for  the  ratio  of  the  opposite  side  to  the  hypotenuse ; 
thus  the  sine  of  the  angle  of  incidence  i  is  BC/BO,  and  the  sine  of  the 
angle  of  refraction  r  is  AD/ AO.  Since  AO  =  BO  by  construction, 


sine  of  Z  i        BC/BO 


BC 


sine  of  Z  r       AD/AO       AD 


=  index  of  refraction. 


450.  Refraction  of  light  by  glass.  We  may  also  show  that 
a  beam  of  light  is  refracted  in  passing  from  air  into  glass. 

Let  a  block  of  glass  of  semicircular  shape  be  attached  to  an  optical 
disk,  as  shown  in  figure  511.  It  will  be  seen  that  part  of  the  ray  is  re- 
flected by  the  glass  as  if  it  were  a  mirror,  and  part  is  refracted  toward 
the  perpendicular  as  it  passes  into  the  glass.  It  will  also  be  seen  that 
the  angle  of  incidence  is  equal  to  the  angle  of  reflection,  but  is  greater 
than  the  angle  of  refraction.  We  may  measure  the  perpendicular  dis- 
tances to  the  normal  from  the  ends  of  the  incident  and  refracted  rays 
as  seen  on  the  disk,  and  compute  the  index  of  refraction  for  glass  and  air. 


SPEED    OF   LIGHT 


489 


Ray  partly 
reflected  and  partly 
refracted  by  glass. 


Ordinary  crown  glass  bends  a  ray  of  light  less  —  that  is,  has 
a  smaller  index  of  refraction  —  than  glass  made  with  lead, 
known  as  flint  glass.  The  lead  glass,  which  _^_ 

is  denser,  has  an  index  of  refraction  with 
respect  to  air  of  about  1.7 ;  while  that  of 
crown  glass  and  air  is  about  1.5. 

In  general,  light  is  bent  in  passing  ob- 
liquely from  one  substance   into   another 
as  from  air  to  glass,  diamond  to  air,  or  even 
from  vacuum  to  air  or  from  a  layer  of  air 
of  one  density  to  one  of    another.     Thus 
light  is  refracted  in  passing  through  the    Fig.  511 
rising  column   of   warm  air  over  a  stove, 
and  things  seem  to  shimmer  or  dance  about. 
The  general  rule  is  that  when  light  enters  a  denser  substance 
obliquely,  it  is  bent  toward  the  perpendicular. 

451.  Refraction  of  sunlight.     An  interesting  case  of  refraction  of 
light   occurs   in    the    atmosphere    surrounding    the    earth.     The   air 

extends  only  a  few  miles  above  the 
y-**s        surface  of  the  earth,  thinning  out  as 
it  goes,  and  beyond  is  empty  space. 
So   when   a   ray   of   sunlight,  SO  in 
figure  512,  comes  through  the  air  ob- 
liquely,   it  is  bent  gradually  toward 
the  normal  in  passing  from  one  layer 
to  another ;   the  result  is  that  the  eye 
at  0  sees  the  sun  in  the  direction  OS', 
Fig.  512.    Refraction  by  the  earth's  instead  of  in  its  real  position.      For 
atmosphere.  this  reason  the  heavenly  bodies  rise 

somewhat  earlier  and  set   somewhat 

later  than  they  would   if   this  were  not  the  case.      This  makes  the 
day  some  7  or  8  minutes  longer. 

452.  Speed  of  light  through  space.     The  reason  for  the  refraction 
of  light  was  not  understood  until  the  velocity  of  light  in  different  sub- 
stances had  been  determined.     Indeed,  up  to  1675  it  was  believed 
that  light  travelled  instantaneously;    that  is,  that  light  consumed  no 
time  in  its  passage  between  two  points.     About  that  time  Roemer,  a 
young  Danish  astronomer  at  the  Paris  Observatory,  was  observing  the 


490  LENSES   AND  OPTICAL  INSTRUMENTS 

moons  of  Jupiter.  With  great  precision  he  observed  just  when  one 
of  the  satellites  M  (Fig.  513)  passed  into  the  shadow  cast  by  Jupiter  «/. 
The  beginnings  of  these  successive  eclipses  of  Jupiter's  satellite  may  be 
thought  of  as  signals  flashed  at  equal  intervals.  When  the  earth  is 
traveling  away  from  Jupiter,  the  observed  interval  between  signals  is 
greater  than  the  true  interval,  because  the  light  from  each  succeeding 
signal  has  a  greater  distance  to  travel  to  reach  the  earth.  But  when 
we  are  traveling  toward  Jupiter,  the  observed  interval  between  signals 
is  less  than  the  true  interval,  because  the  light  from  each  succeeding 
signal  has  a  shorter  distance  to  travel  to  reach  the  earth.  Thus  while 

the  earth  is  travel- 
ing from  A  to  B, 
the  observed  times 
of  the  eclipses  are 
delayed  more  and 

vv-:- vj.-™rrrj^j^,        more,  and  when  the 

,___- — -""""        jf    •*"       earth  has  reached 
'  B,  the  total  delay 

has   amounted   to 
16     minutes     and 
Fig.  513-     lUustrating  Roemer's  way  of  measuring  speed    36  seconds  (about 

1000    seconds). 

This  means  that  it  takes  about  1000  seconds  for  the  light  to  travel 
across  the  earth's  orbit,  a  distance  of  186,000,000  miles.  Therefore 
the  velocity  of  light  is  186,000  miles  per  second  (300,000  kilometers 
per  second).  In  recent  years  the  velocity  of  light  has  been  directly 
measured  with  great  precision  on  the  earth's  surface  by  several 
methods,  and  the  results  agree  very  closely  with  those  obtained  so 
long  ago  by  Roemer. 

This  velocity  is  so  enormous  that  it  is  not  strange  that  the  earlier 
experimenters  could  not  determine  it.  In  fact,  it  takes  only  0.001  of  a 
second  for  light  to  travel  as  far  as  one  can  see  on  the  earth.  Light 
travels  a  very  little  more  slowly  in  air  than  in  a  vacuum.  In  denser 
substances,  such  as  water  and  glass,  light  travels  much  more  slowly. 

453.  Light  waves.  Just  as  we  think  of  sound  as  trans- 
mitted from  a  source  through  the  air  by  a  series  of  waves,  so  we 
think  of  light  as  transmitted  through  space  by  a  series  of  ether 
waves.  When  the  light  comes  from  a  point  source,  the  spherical 
crest,  or  wave  front,  of  each  wave,  spreads  in  all  directions  with 
equal  velocity,  and  the  direction  of  advance,  being  radial,  is  at 


WHY  LIGHT  IS   REFRACTED 


491 


Fig.  514.     Wave  fronts. 


right  angles  to  the  wave  front.     Such  a  series  of  expanding 

waves  is  shown  in  figure  5 14 (a),  in  which  the  curved  lines  are 

the  wave  fronts  and  the  lines   of 

arrows  indicate  the  direction  of  ad- 
vance of  small  sections  of  the  wave 

front.     These  lines  of  advance  are    o* 

what  were  called  rays  in  the  last 

chapter.      A  bundle  of    rays    is   a 

beam.     In  a  "parallel  beam"  (Fig. 

514(6))  the  wave  fronts  are  plane 

and  the  rays  are  parallel. 

By  means  of  a  lens  or  curved  mir- 
ror, a  beam  of  light  may  be  made 

to  converge  toward  a  point,  called 

the  focus.      In  this  case  the  wave 

fronts  are  concave  spherical  surfaces     B* 

which   contract   as    they   approach 

the  focus  (Fig.  514(c)). 
454.   Why  light  is  refracted.     When  a  beam  of  light  passes 

from  air  into  water,  there  is  a  change  in  its  velocity.     To  show 

how  this  causes  a  refraction  of  the 
beam,  let  the  parallel  lines  in  figure 
515  represent  wave  fronts  advancing 
in  the  direction  of  the  arrows.  As 
soon  as  the  edge  B  of  a  wave  front 
enters  the  water,  it  begins  to  advance 
slowly,  while  the  part  A,  which  is  still 
in  the  air,  advances  with  the  same 
speed  as  before.  Consequently  the 
direction  of  the  wave  front  is  changed 
into  the  position  CD,  and  the  beam 

Fig.   515.     Diagram  to  show  is  bent  into  a  direction  nearer  the 
cause  of  refraction.  perpendicular  PR. 

This  is  somewhat  analogous  to  a  column  of  soldiers  marching  from 
a  smooth,  hard  field  into  a  rough,  plowed  field,  where  they  are  slowed 


492  LENSES  AND  OPTICAL  INSTRUMENTS 

up.  The  man  at  B  hits  the  rough  ground  before  the  man  at  A  does, 
and  so,  while  A  travels  the  distance  AC,  B  has  gone  a  shorter  distance 
BD.  The  result  is  that  if  B  cannot  hurry,  and  if  A  does  not  slow  up, 
the  column  swings  around  from  its  original  direction  into  one  nearer 
the  perpendicular  PR. 

When  a  beam  of  light  enters  water  perpendicular  to  the  surface, 
it  suffers  no  refraction.  The  change  in  velocity  is,  of  course,  just 
the  same  whether  the  light  enters  normally  to  the  surface  or 
obliquely  ;  but  bending,  or  refraction,  occurs  only  when  the  light 
enters  obliquely. 

455.  Speed  of  light  and  index  of  refraction.  From  figure 
515  it  will  be  seen  that  the  amount  which  the  beam  of  light 
is  refracted  when  passing  from  air  into  water  depends  upon 
the  relation  between  the  distances  AC  and  BD;  that  is,  upon 
the  relation  between  the  speed  of  light  in  air  and  its  speed  in 
water.  Although  it  is  not  easy  to  measure  the  speed  of  light  in 
water,  yet  it  has  been  done.  The  speed  in  water  has  been 
proved  to  be  about  three  fourths  that  in  air.  This  means  that 
the  speed  of  light  in  air  is  1.33  times  the  speed  in  water,  which 
is  the  same  number  that  we  found  from  the  index  of  refraction 
of  water  and  air.  In  general 

Index  of  refraction  = speed  in  air 

speed  in  other  substance 

We  may  prove  this  as  follows : 

Index  of  refraction  =-?  ^r(see  section  449). 

But  i  is  equal  to  the  angle  ABC  (Fig.  515),  and  sin  ABC  =  AC/BC  ; 
also  r  is  equal  to  the  angle  BCD,  and  sin  BCD  =  BD/BC. 
Therefore, 

sini       AC/BC      AC         speed  in  air 

—. —  =   prt/pr>  =  BTi  =  — ^~j~- r—  =  index  of  refraction. 

sm  r       BD/BC      BD      speed  in  water 

456.  Total  reflection.  We  have  seen  in  section  448  that 
when  a  beam  of  light  passes  obliquely  from  water  or  glass  into 
air,  the  refracted  ray  is  bent  away  from  the  perpendicular. 


TOTAL   REFLECTION 


493 


516.     Critical  angle  and  total  re- 
flection of  light  by  water. 


For  example,  in  figure  516  the  light  coming  from  a  point  0 
under  water,  in  the  direction  oa,  is  refracted  in  the  direction 
aar  ;  the  ray  ob  is  refracted 
along  bb  '  and  oc  is  refracted 
along  cc'.  As  the  angle  in  the 
water  increases,  we  come  finally 
to  a  ray  vd  which  is  refracted 
along  dd',  and  just  grazes  the 
surface  of  the  water.  The 
.  angle  which  is  formed  between 
the  ray  od  and  the  normal  NM 
is  called  the  critical  angle. 
For  water  and  air  it  is  about 
49°.  If  this  angle  is  exceeded,  as  in  the  case  of  the  ray  oe,  the 
ray  cannot  leave  the  water  at  all,  but  is  totally  reflected  at  e, 
just  as  if  it  had  fallen  on  a  polished  metal  surface,  and  takes 
the  direction  ee'. 

The  critical  angle  is  the  angle  in  the  denser  medium  which  must 
not  be  exceeded  if  the  ray  is  to  get  out. 

To  illustrate  total  reflection,  we  may  hold  a   tumbler   containing 
water  and  a  spoon  above  the  eye,  and  look  up  at  the  surface  of  the  water. 

A  very  bright  image  of 
the  part  of  the  spoon 
in  the  water  will  be 
seen  by  total  reflection. 
If  the  apparatus 
shown  in  figure  517  is 
available,  the  paths  of 
various  refracted  and 
reflected  rays,  includ- 
ing some  that  are 
totally  reflected,  can 
be  studied  with  great 
ease 


Fig.  517.    Apparatus  showing  refraction  and  reflec- 
tion  of  light  by  water  in  a  tank. 


457.  A  prism  as  a  mirror.  In  optical  instruments  it  is  frequently 
necessary  to  have  a  very  perfect  reflector,  and  for  this  purpose  a  right- 
angle  prism  with  polished  sides  is  used.  Let  a  ray  of  light  A  B  strike 


494 


LENSES  AND  OPTICAL  INSTRUMENTS 


the  side  XZ  of  such  a  prism  (Fig.  518)  at  right  angles.     It  suffers  no 
refraction,  but  passes  on  through  the  glass  to  B  on  the  side  YZ,  where 
it  makes  an  angle  of  45°  with    the    normal  mn. 
»(i  yj  But  the  critical  angle  for  crown  glass  is  about  42° ; 

therefore  the  ray  AB  does  not  emerge  from  the 
.A  glass,  but  is  totally  reflected  in  the  direction  BC. 
It  then  strikes  the  face  XY  perpendicularly  and 
emerges  without  refraction.  The  result  is  that  the 
ray  is  bent  90°,  as  if  there  had  been  a  plane  mirror 
at  YZ. 

458.  Refraction  by  plate  with  parallel  sides. 
When  a  ray  of  light  (A B  in  figure  519)  passes 
through  a  glass  plate  with  parallel  faces,  such  as 
a  good  window  pane,  it  is  refracted  at  B  toward  the  normal  BN,  and 
at  C  away  from  the  normal  CM.  The  result 
is  that  the  ray  CD  is  parallel  to  the  ray  A  B. 
Consequently  when  we  look  at  any  object 
through  a  glass  plate,  we  see  it  slightly  dis- 
placed in  position,  but  otherwise  unchanged. 

When  the  plate  is  thin,  this  change  of  posi-  '\!  ^   ;    mate 

tion  is  too  slight  to  attract  attention.  ~ —  ^  NAI "Glass 


c 

Fig.  518.  Total  re- 
flection of  light  by 
a  right-angle  prism. 


459.  Refraction  by  a  prism.     When 
a  ray  XY  enters  one  side  of  a  prism 
ABC  as  shown  in  figure  520,  it  is  bent 
in  the  direction  YZ;  and  on  emerging,  Fig.  519.   Path  of  ray  through 
it  is  again  bent  in  the  direction  ZW.  plate  glass 

Thus  the  ray  XO  is  bent  out  of  its  original  course  to  X'W . 

The  total  change  of  direction  is 
measured  by  the  angle  XOX',  called 
the  angle  of  deviation.  Any  sub- 
stance which  has  two  plane  refract- 
ing surfaces  inclined  to  each  other 
is  a  prism.  The  angle  A  is  called 
Fig.  520.  Refraction  of  light  by  the  refracting  angle  of  the  prism. 

a  prism-  The  path  of  a  ray  of  light  through 

a  prism  can  be  found  by  drawing  a  diagram,  like  figure  510, 
at  Y  and  again  at  Z.  It  should  be  remembered  that  the  beam 
is  always  bent  toward  the  thicker  part  of  a  prism. 


LENSES,   CONVERGENT  AND   DIVERGENT  495 

QUESTIONS  AND  PROBLEMS 

(The  student  should  have  a  small  protractor.) 

1.  In  what  direction  must  a  fish  look  to  see  the  setting  sun  ? 

2.  Explain  with  a  diagram  how  atmospheric  refraction  increases  the 
length  of  daylight. 

3.  If  the  angle  of  incidence  of  a  ray  of  light  passing  from  air  into 
glass  is  68°,  and  the  angle  of  refraction  is  36°,  find  by  construction  the 
index  of  refraction. 

4.  If  the  index  of  refraction  for  air  and  water  is  1.33,  and  the  larger 
angle  is  60°,  find  by  construction  the  smaller  angle. 

6.    Taking  the  index  of  refraction  as  1.33,  find  by  construction  the 
critical  angle  for  water. 

6.  If  the  critical  angle  for  crown  glass  is  42°,  find  by  construction 
the  index  of  refraction. 

7.  Assuming  the  velocity  of  light  in  air  to  be  about  186,000  miles 
per  second  and  the  index  of  refraction  of  flint  glass  to  be  1.6,  compute 
the  velocity  of  light  in  flint  glass. 

8.  The  angles  of  a  prism  are  20°,  70°,  and  90°.     A  ray  of  light 
enters  normally  the  face  bounded  by  the  angles  90°  and  70°.     The 
glass  has  a  critical  angle  of  42°.     Prove  that  the  ray  will  be  twice  re- 
flected before  it  leaves  the  prism. 

9.  Will  a  beam  of  light  going  from  water  into  crown  glass  be  bent 
toward  or  away  from  the  perpendicular? 

10.  Experiments  show  that  when  light  passes  from  air  into  water, 
it  is  bent  less  than  when  it  passes  from  air  into  carbon  bisulfide  at  the 
same  angle  of  incidence.  Is  the  speed  of  light  in  carbon  bisulfide  greater 
or  less  than  in  water  ? 

LENSES 

460.  Lenses,  convergent  and  divergent.  A  lens  is  a  piece 
of  glass,  or  other  transparent  substance,  with  polished  spheri- 
cal surfaces.  A  straight  line  drawn  through  the  centers  Ci 
and  C2  (Fig.  521)  of  the  two  spherical  surfaces  is  called  the 
principal  axis  of  the  lens. 

Lenses  are  divided  into  two  classes,  converging  or  "  thin- 


496 


LENSES  AND  OPTICAL  INSTRUMENTS 


edged "  lenses   (Fig.   521),   and   diverging  or   "  thick-edged  " 
lenses  (Fig.  522).     A  converging  lens  is  thinner  at  the  edge 

than  in  the  center.  A 
common  type  of  this 
class  is  the  double  convex 
lens.  A  diverging  lens 
is  thicker  at  the  edge 
than  at  the  center.  The 


Piano 
Convex 


Converging 
Meniscus 


Fig.  521.     Converging  (thin-edged)  lenses. 


double    concave    lens    is 
a  common  lens  of   this 


class.  It  should  be  remembered  that  when  a  ray  of  light 
passes  through  a  lens,  it  is  always  bent,  just  as  in  a  prism, 
toward  the  thicker 
part  of  the  lens. 

461.  Action  of 
a  convex  lens,  if 
we  hold  a  double 
convex  lens  so  that 
the  sunlight  (or  some 
other  source  of  par- 
allel rays)  comes  to 

it  along  its  principal  axis,  we  find  that  the  light  is  refracted  so  as  to 
converge  nearly  at  one  point.  If  a  piece  of  paper  is  Jj^ld  at  this  point, 
a  small  but  very  bright  image  of  the  sun  is  formed  and  the  paper  is 

quickly  charred.     The  thicker  the  lens,  the  nearer 

is  this  point,  called  the  focus,  to  the  lens. 

The  optical  disk  may  be  used  here  to  show 

the   action   of  a  convex   lens   on  parallel   rays 

(Fig.  523). 


522.     Diverging  (thick-edged)  lenses. 


The  point  where  rays  parallel  to  the  prin- 
cipal axis  converge  is  called  the  principal  focus 
of  a  lens.  A  lens  has  a  principal  focus  on 
each  side,  and  the  two  are  equidistant  from 
optical  disk  the  lens.  The  distance  from  the  lens  to 
either  principal  focus  is  called  the  focal  length 


Fig.  523 

used  to  show  ac- 
tion of  converging 
lens. 


of  the  lens. 


FORMATION  OF  IMAGES   BY   LENSES 


497 


Since  an  incident  ray  and  its  corresponding  refracted  ray  are 
reversible,  it  follows  that  a  light,  placed  at  the  principal  focus, 
would  send  its  rays  through  the  lens  in  such  a  way  as  to  come 
out  parallel. 

For  an  ordinary  double  convex  lens  with  its  two  surfaces  of  the 
same  curvature  and  made  of  glass  whose  index  of  refraction  is  about 
1.5,  the  focal  length  is  equal  to  the  radius  of  curvature.  If  one  sur- 
face is  plane,  the  focal  length  is  double  the  radius  of  curvature. 

462.   Change  of  wave  front  produced  by  a  convex  lens.     We 

have  already  learned  that  light  travels  more  slowly  in  glass  than 
in  air  (section  455) .  The  light 
waves  from  the  sun  or  a  dis- 
tant object  are  practically 
plane  waves  when  they  strike 
the  lens.  The  successive  posi- 
tions and  shapes  of  the  ad- 
vancing waves  are  shown  in  Fig.  524. 
figure  524  by  lines  drawn 
across  the  beam.  It  will  be  seen  'that  the  central  portion  of 
these  waves  is  retarded  more  than  the  outer  portions  in  passing 
through  the  lens.  Therefore  the  light  waves  on  emerging  from 
the  lens  have  a  concave  front.  As  light  waves  move  at  right 

angles  to  the  front  of 
the  wave,  the  light  is 

m)  (I  brought    to   a   focus ; 

but  after  passing  the 
focus  the  waves  have 
a  convex  front. 

463.   Formation    of 
images  by  lenses,    if 


Action  of  a  converging  lens  on 
a  plane  wave  front. 


Fig.  525- 


Formation  of  an  image  on  a  screen  by 
a  convex  lens. 


we  place  a  luminous  ob- 
ject, such  as  an  electric 
lamp,  near  a  convex  lens  but  beyond  its  principal  focus,  the  light  rays 
from  the  object  will  be  brought  to  a  focus  on  the  other  side  of  the  lens, 
and  the  image  of  the  lamp  may  be  clearly  seen  upon  a  screen  placed 
at  this  point  (Fig.  525).  It  will  be  noticed  that  the  image  is  inverted 


498 


LENSES   AND  OPTICAL  INSTRUMENTS 


and  larger  than  the  object.  If  we  interchange  the  position  of  the 
object  (lamp)  and  the  image  (screen),  or  do  what  amounts  to  the  same 
thing,  interchange  the  object-distance  and  image-distance  by  moving 
the  lens  nearer  the  screen,  we  find  another  position  of  the  lens  which 
gives  a  clear  inverted  image  but  one  smaller  than  the  object.  We  may 
move  the  screen  farther  away  from  the  lamp  and  again  find  two 
positions  for  the  lens  which  give  sharp,  distinct  images. 

Two  points  so  situated  on  opposite  sides  of  a  lens  that  an  object 
at  one  will  form  an  image  at  the  other  are  called  conjugate  foci. 

464.  Equation  for  convex  lenses.  The  relative  positions  of 
an  object  and  its  image  formed  by  a  convex  lens  are  determined 
by  the  focal  length  of  the  lens.  The  relation  between  the 
distance  of  the  object  from  the  lens,  the  distance  of  its  image 
from  the  lens,  and  the  focal  length  (when  the  lens  is  thin)  is 
given  by  the  same  equation  as  for  mirrors  (section  446)  : 


Do      Dj       f 

where  Do  =  distance  of  object  from  lens, 

Dj  =  distance  of  image  from  lens, 
/  =  focal  length  of  lens. 

465.    Discussion  of  the  lens  formula.     If  the  object  is  so  far  away 
that  the  rays  from  any  point  of  it  to  different  parts  of   the  lens  are 
Lens  practically  parallel,  the  image 

is  formed  at  F;  for  D0  is  very 

large,  and  so  -^-  is  nearly  zero ; 

this  leads  to  Dl  =  f  (Fig.  526). 
If    the    object    is    brought 
nearer    the    lens,    the    image 
When  Do  =  2/,  Dl  =  2f  also, 


Fig.  526.    Image  of  distant  object  is  at  F. 
moves  farther  away  from  the  lens. 


as  shown  in  figure  527. 

If  the  object  is  brought  still  nearer  the  lens,  the  image  moves  still 


Fig.  527.    Image  at  same  distance  as  object. 


CONSTRUCTION  OF  IMAGES  FORMED  BY  LENSES     499 


farther  away  from  the  lens,  until,  when  the  object  is  at  the  principal 
focus  F,  the  distance  of  the  image  becomes  infinitely  great,  and  the 
rays  that  go  out  from  the  lens  are  parallel  (Fig.  528). 

If  the  object  is  brought  even  nearer  the  lens  (inside  the  principal  focus), 
the  rays  on  the  farther  side  diverge  as  if  they  came  from  a  focus  7  be- 


k  ----  Do-f  -----  >• 


—  oo 


negative 
Fig.  528.     Object  at  F,  rays  parallel.     Fig.  529.     Object  inside  F,  image  virtual. 

hind  the  lens  (Fig.  529).  In  this  case,  Di  in  the  formula  is  negative. 
This  means  that  the  image  is  behind  the  lens,  that  is,  on  the  same  side 
of  the  lens  as  the  object. 

466.  Construction  of  images  formed  by  lenses.  The  geometrical 
construction  of  images  formed  by  lenses  will  indicate  the  size  and  posi- 
tion of  these  images.  The 
method  of  procedure  is 
the  same  as  that  used  for 
spherical  mirrors  (section 
441).  If  we  trace  two 
rays  from  any  point  of 
the  object  to  their  inter- 
section,  we  have  the  posi-  Fi*'  53<>.  Size  of  real  image, 

tion  of  the  corresponding  point  of  the  image.  For  example,  in  figure 
530,  a  ray  from  A  parallel  to  the  principal  axis  must,  after  refraction 
by  the  lens,  pass  through  the  principal  focus  F.  Another  ray  from  A, 
passing  through  the  center  of  the  lens,  is  undeviated.  The  point  A ' 
where  these  rays  meet  is  the  image  point  of  A.  Then  from  similar 
triangles  it  is  readily  seen  that 

Length  of  image  _  distance  of  image  from  lens 
Length  of  object  ~~  distance  of  object  from  lens 

The  ratio  of  the  length  of  the  image  to  the  length  of  the  object  is  called 
the  linear  magnification. 

In  figure  530  the  object  AB  is  beyond  the  principal  focus  of  the 
convex  lens,  and  the  image  A 'B'  is  inverted,  real,  and,  in  this  case, 
smaller  than  t,he  object. 


500 


LENSES  AND   OPTICAL  INSTRUMENTS 


Lens 


In  figure  531  the  object  AB  is  between  the  principal  focus  F  and  the 
lens.     The  image  A'B'  is  erect,  virtual,  and  larger,  and  can  be  seen 

only  by  looking  through 
the  lens.  A  virtual  im- 
age cannot  be  projected 
upon  a  screen  as  a  real 
image  can. 

467.  Image  in  a 
concave  lens.  When 
a  series  of  rays  paral- 
lel to  the  principal 


Fig.  531.     Size  of  virtual  image. 


axis  pass  through   a 
concave    lens,     they 

emerge  as  divergent  rays  and  appear  to  be  coming  from  the 

point  which  is  called  a  virtual  focus. 

We  may  demonstrate  this  divergent  action 
of  a  concave  lens  by  means  of  an  optical  disk, 
as  shown  in  figure  532. 

To  explain  this  phenomenon,  we  have 
only  to  imagine  a  series  of  plane  waves 
striking  a  concave  lens.  Since  it  is  thinner 
at  the  center  than  at  the  edges,  the  middle 
of  the  wave  is  retarded  less  by  the  glass  than 
its  ends.  The  emergent  wave  front  is  convex 
and  forms  a  diverging  cone  of  light  which 
proceeds  as  if  coming  from  the  virtual  focus.  of  a  diverging  lens. 

Figure  533  shows  the  geometrical  method  of  constructing  and  lo- 
cating the  image  in  a  concave  lens.  It  will  be  seen  that  the  image  is 
apparently  on  the  same  side  of  the  lens  as  the  object,  and  is  virtual, 

erect,  and  smaller  than  the 
object.  In  applying  the  lens 
equation  to  concave  lenses, 
the  focal  length  is  considered 
negative ;  therefore  a  concave 
lens  is  often  called  a  minus 

Virtual  image  formed  by  a  concave    (-)  lens,  while  a  convex  lens 
lens.  is  a  plus  (+)  lens. 


Fig.    532.    Optical  disk 
used  to  show  action 


Fig.  533 


DEFECTS  OF  IMAGES  501 

468.  Defects  of  images  formed  by  lenses.  In  the  construc- 
tion of  figure  530  it  is  assumed  that  all  the  rays  coming  from  a 
point  in  the  object  are  accurately  refracted  by  the  lens  to  one 
point.  But  as  a  matter  of  fact  the  rays  that  strike  the  outer 
portions  of  a  lens  are  refracted  more  than  the  rays  which  fall  on 
the  central  portion  of  the  lens,  and  so  come  to  a  focus  nearer  to 
the  lens.  This  is  called  spherical  aberration. 

This  may  easily  be  demonstrated  by  forming  the  image  of  an  electric 
arc  on  a  distant  screen  by  means  of  the  condensing  lenses  of  an  ordinary 
projecting  lantern  (section  474).  The  image  will  be  blurred.  But 
if  the  lens  is  covered  except  for  the  central  portion,  the  image  will 
be  sharp.  Try  the  effect  of  covering  the  lens  except  for  a  narrow 
circular  zone  equally  distant  from  the  center.  How  must  the  lens 
be  moved  to  give  a  sharp  image  when  the  zone  is  used  ? 

The  effects  of  spherical  aberration  are  to  make  the  image 
indistinct  and  to  distort  -its  shape.  If  the  outer  rays  are  cut 
out  by  means  of  a  diaphragm,  or  stop,  the  sharpness  of  the  image 
is  improved,  but  at  the  same  time  its  brightness  is  diminished. 
In  large  lenses,  such  as  those  used  in  telescopes,  the  outer 
portions  are  so  ground  that  their  refracting  power  is  diminished 
by  the  proper  amount  to  insure  distinct  miages. 

This  whole  geometrical  theory  of  lenses  applies  to  only  very 
thin  lenses,  and  to  cases  where  the  light  may  be  assumed  to 
pass  through  the  lens  in  a  direction  not  greatly  inclined  to  the 
axis  of  the  lens.  In  practice,  combinations  of  lenses  are  nearly 
always  used  instead  of  simple  lenses,  and  these  combinations 
are  designed  so  that  the  imperfections  of  one  lens  are  compen- 
sated for  or  balanced  by  the  imperfections  of  another  lens. 

QUESTIONS  AND  PROBLEMS 

1.  A  convex  lens  has  a  focal  length  of  16  centimeters.      Find  the 
position  and  nature  of  the  images  formed  when  objects  are  placed  10 
meters,  50  centimeters,  and  10  centimeters  respectively  from  the  lens. 

2.  If  an  object  is  placed  32  centimeters  from  the  lens  described  in 
problem  1,  how  far  is  the  image  from  the  lens? 

3.  A  lamp  placed  60   centimeters  from  a  lens  forms  a  distinct 


502 


LENSES  AND   OPTICAL  INSTRUMENTS 


image  on  a  screen  20  centimeters  away  on  the  other  side.  Find  the 
focal  length  of  the  lens. 

4.  A  double  convex  lens  used  as  a  reading  glass  has  a  focal  length  of 
15  inches  and  is  held  10  inches  from  the  book.  What  is  the  distance  of 
the  image  from  the  lens  ? 

6.  What  is  the  ratio  of  the  length  of  the  image  formed  in  problem 
4  to  the  length  of  the  object  ? 

6.  Is  it  true  for  both  mirrors  and  lenses  that  real  images  are  always 
inverted  f 

7.  A  small  object  moves  along  the  principal  axis  of  a  convex  lens 
toward  the  lens.     Describe  the  changes  in  the  position  and  size  of  the 
image.     Is  the  image  real  or  virtual  ? 

8.  At  what  distance  from  a  convex  lens  must  an  object  be  placed 
in  order  that  the  image  maybe  hah3  as  long  as  the  object?     Focal 
length  of  lens  is  30  centimeters. 

9.  At  what  distance  from  a  convex  lens  must  an  object  be  placed 
in  order  that  the  image  may  be  twice  as  long  as  the  object?     Focal 
length  of  lens  is  24  centimeters. 

10.  An  object  is  30  centimeters  from  a  lens,  and  its  image  is  3 
centimeters  from  the  lens  on  the  same  side.  Is  the  lens  convex  or 
concave  ?  What  is  its  focal  length  ? 

OPTICAL  INSTRUMENTS 

469.  Photographic  camera.  A  camera  is  merely  a  light- 
tight  box  (Fig.  534)  with  a  converging  lens  at  one  end,  so 

mounted  as  to  form  an  image 
of  an  outside  object  upon  a 
"  sensitized  "  plate  or  film  at 
the  other  end.  This  plate  con- 
sists of  a  silver  compound  spread 
on  a  glass  plate  or  celluloid 
sheet  (film).  The  light  is  al- 
lowed to  pass  through  the  lens 
for  a  time  which  varies  from  a 
thousandth  of  a  second  up  to 
several  minutes,  according  to 
the  lens,  the  brightness  of  the 
Fig.  534.  A  folding  pocket  camera,  object  to  be  photographed,  and 


Finder 


Shutter 


THE  EYE  503 

the  "speed"  of  the  sensitized  plate.  The  image  on  the  plate 
is  not  visible  until  the  plate  is  placed  in  a  mixture  of  chemicals 
called  a  developer. 

To  obviate  the  spherical  aberration  of  a  single  lens,  a  dia- 
phragm is  put  in  front  of  the  lens  in  order  to  limit  the  size  of 
the  pencil  of  light.  With  a  small  opening,  or  stop,  we  get 
great  sharpness  in  the  picture,  but  must  expose  it  for  a  longer 
time.  A  "  combination  lens,"  with  the  diaphragm  between  the 
two  lenses,  is  used  to  take  clear  pictures  of  rapidly  moving 
objects.  Since  the  plate  on  which  the  image  is  formed  must  be 
in  the  position  which  is  the  conjugate  focus  of  the  position  occu- 
pied by  the  object,  the  camera  is  usually  made  with  a  bellows 
so  that  it  can  be  "  focused  "  on  objects  at  varying  distances. 

470.  The  eye.  The  human  eye  (Fig.  535)  is  essentially  a 
little  camera,  with  a  lens  system  in  front,  and  a  sensitive  film, 
made  of  nerve  fibers,  at  the  back. 

It  has  the  great  advantage  over  any  other  camera  in  that 
it  can  take  a  continual  succession  of  pictures  all  on  the  same 
film,  "  developing "  them  in- 
stantaneously by  some  unknown 
chemical  or  electrical  process  in 
the  nerve  fibers,  and  transmit- 
ting the  results  equally  instan-  pupi 
taneously  over  a  "  private  wire  " 
(the  optic  nerve)  to  "  head- 
quarters "  (the  brain). 

The  structure  of  the  eye  is 
shown  in  figure  535.     There  is 

1  ,        Fig.  535.     Section  of  the  human  eye. 

an  outer  horny  membrane,  the 

cornea,  holding  a  watery  fluid  called  the  aqueous  humor. 
There  are  also  an  adjustable  diaphragm,  or  stop,  called  the 
iris,  and  a  crystalline  lens.  The  latter  has  a  somewhat  higher 
index  of  refraction  than  either  the  aqueous  humor  in  front  or 
a  similar  fluid,  the  vitreous  humor,  behind.  At  the  back  is  the 
nerve  layer,  or  retina,  which  acts  as  the  sensitized  film. 


504 


LENSES  AND  OPTICAL  INSTRUMENTS 


It  should  be  noticed  that  most  of  the  converging  power  of  the  eye 
comes,  not  in  the  lens,  but  at  the  front  surface  of  the  cornea.  This 
explains  why  we  can  never  see  objects  distinctly  when  swimming  under 
water.  The  aqueous  fluid  and  the  water  outside  are  so  much  alike  that 
there  is  no  longer  any  refraction  of  the  light  as  it  strikes  the  cornea ; 
and  the  lens  by  itself  is  not  powerful  enough  to  bring  the  light  to  a 
sharp  focus  on  the  retina. 

471.  Focusing  the  eye.     If  an  object  is  moved    nearer  a  camera, 
the  distance  between  the  plate  and  lens  must  be  increased ;   or  else  a 
lens  of  greater  convexity,  that  is,  of  shorter  focus,  must  be  substituted, 
if  the  picture  is  to  be  sharp.     Of  these  two  possibilities,  the  eye  chooses 
the  second.     It  adapts  itself  to  varying  distances,  not  by  moving  the 
retina,  but  by  changing  the  focal  length  of  the  lens.     When  the  muscles 
of  the  eye  are  relaxed,  the  lens  is  usually  of  such  a  shape  as  to  focus 
clearly  on  the  retina  objects  which  are  at  a  considerable  distance. 
When  one  wishes  to  look  at  near  objects,  a  ring  of  muscle  around  the 
crystalline  lens  causes  the  lens  to  become  more  convex,  so  as  to  form 
a  distinct  image  on  the  retina.     This  power  of  adjustment  of  the  lens 
of  the  eye  for  objects  at  different  distances  is  called  accommodation. 
It  is  often  said  that  objects  are  seen  most  distinctly  when  held  about 
10  inches  (25  centimeters)  from  the  eye.     This  simply  means  that  10 
inches  is  about  as  near  as  one  can  usually  focus  an  object  distinctly ; 
and  since  the  shortest  distance  gives  the  largest  image,  this  is  where  we 
automatically  hold  an  object  when  we  want  to  see  its  details. 

472.  Imperfections  of  the  eye.     In  the  short-sighted  eye  the  im- 
age of  a  distant  object  is  formed  in  front  of  the  retina  (at  A  in  figure 


—  Lens 
Fig.  536.     A  short-sighted  eye. 


-\-Lvnx 


Fig.  537.     A  far-sighted  eye. 


536).  This  may  be  due  to  too  great  convexity  in  the  crystalline  lens, 
or  to  the  oval  shape  of  the  eyeball.  A  person  who  is  short-sighted 
must  bring  objects  close  to  the  eye  to  see  them  distinctly.  Specta- 
cles with  concave  lenses  are  used  to  correct  short-sighted  eyes. 

In  the  far-sighted  eye  the  image  of  an  object  at  an  ordinary  distance 
would  be  formed  behind  the  retina  (at  B  in  figure  537).  This  is  be- 
cause the  crystalline  lens  is  too  flat,  or  the  length  of  the  eyeball  is  too 


PROJECTING  LANTERN 


505 


short.     To  see  distinctly,  such  a  person  must  hold  objects  at  a  dis- 
tance.    Convex  lenses  are  used  for  far-sighted  eyes.     In  old  age  the 

lens  of  the  eye  loses  its  power  of  accommodation  and  so  requires  a 

convex  lens. 

Another  defect  of  the  eye  is  astigmatism,  which  occurs  when  the  lens 

of  the  eye  or  the  cornea  does  not  have  a  truly  spherical  surface.     The 

effect  is  that  a  spot  of  light,  like  a  star,  is 

seen  as  a  short,  bright  line.     In  a  case  of 

astigmatism  all  the  lines  in  such  a  diagram 

as  figure  538  will  not  appear  equally  distinct. 

Those  in  one  direction  will  be  sharply  defined, 

while   those   at   right  angles    to   them   will 

appear  broadened  and  blurred.     This  defect, 

is  corrected  by  the  use  of  cylindrical  lenses. 
473.    Apparent   distance   and  size.      The 

apparent  size  of  an  object  depends  on  the 

size  of  the  image  formed  on  the  retina,  and 

consequently  on  the  visual  angle. 

From  figure  539  it  is  evident  that  this  angle  increases  as  the  object 

is  brought  nearer  the  eye.    For  example,  when  we  look  along  a  railroad 

track,  the  rails  seem  to  come  nearer 
together  as  their  distance  from  us 
increases.  The  image  of  a  man  100 
yards  away  is  one  tenth  as  large  as 
the  image  of  the  same  man  when  he 
is  10  yards  off.  We  do  not  actually 
interpret  the  larger  image  and  larger 


Fig    538.     Lines  to  test  as- 
tigmatism. 


Fig.  539      The  visual  angle. 


visual  angle  as  meaning  a  larger  man,  because  by  experience  we  have 
learned  to  take  into  account  the  known  distance  of  an  object  in 
estimating  its  size. 

Distant  objects  seen  in  clear  mountain  air  often  seem  nearer  than 
they  really  are.  That  is  because  we  see  the  objects  more  clearly  and 
distinguish  the  details  more  sharply ;  and  this  often  leads  us  to  think 
that  they  are  smaller  than  they  really  are.  The  moon,  on  the  other 
hand,  seems  bigger  when  near  the  horizon  than  when  high  up  in  the  sky, 
because  we  can  compare  it  with  objects  whose  size  we  know.  It  is 
only  by  long  experience  that  we  learn  to  estimate  the  actual  size  and 
distance  of  objects. 

474.  Projecting  lantern.  The  projecting  lantern,  or  stere- 
opticon,  is  used  to  throw  an  image  of  a  brilliantly  illuminated 
object  or  picture  upon  a  screen.  It  consists  essentially  of  a 


506 


LENSES   AND  OPTICAL  INSTRUMENTS 


Fig.  540.     A  projecting  lantern  for  slides. 

powerful  source  of  light,  such  as  an  electric  lamp  A  (Fig.  540), 
two  condensing  lenses  C,  which  converge  the  light  through  the 
slide,  or  transparent  picture,  S,  and  a  combination  front  lens,  or 

objective,  L,  which  forms  a  real 
image  of  the  picture  on  the  screen  S'. 
It  will  be  noticed  that  the  lantern 
is  much  like  the  camera  except  that 
the  object  and  image  have  been 
interchanged.  Since  the  screen  is 
usually  at  a  considerable  distance, 
the  slide  S  is  only  a  little  beyond  the 
principal  focus  of  the  objective  L. 
It  is  very  important  to  have  a 
powerful  light  source  which  is  small 
in  size.  For  this  purpose  an  elec- 
tric arc  or  an  electric  glow  lamp, 
in  which  the  filament  is  coiled  into 
a  small  space,  is  generally  used. 

475.    Motion  pictures.     The  motion- 
picture  camera  (Fig.  541)  takes  a  series 
of  pictures  on  a  long  narrow  film.     The 
camera  is  operated  by  a  crank  so  that  it 
opens  and  closes  the  shutter  about  16 
times  a  second.     The  film  moves  a  little 
while  the  shutter  is  closed,  but  remains 
A   motion-picture      stationary  while  it  is  open.    The  pictures 
camera.  (Fig.  542)  are  about  f  of  an  inch  high 


MOTION   PICTURES 


507 


Fig.  542. 


A  section  of  a  motion-picture  film,  showing  Tilden,  the  tennis  player, 
in  action. 


508 


LENSES   AND  OPTICAL  INSTRUMENTS 


and  about  1  inch  wide.  The  films  are  made  up  in  reels  of  about  1000 
feet  each,  and  since  about  1  foot  of  film  moves  past  the  lens  every 
second,  one  reel  of  film  contains  about  16,000  pictures.  Each  picture 
of  such  a  series  differs  slightly  from  the  preceding  one,  if  anything  is 


Fig-  543-    A  motion-picture  projector  with  diagram  of  some  essential  parts. 

moving  in  the  field  of  the  camera.  From  such  a  series  of  negatives 
any  number  of  reels  of  positives  may  be  printed  for  projection  pur- 
poses. By  means  of  a  special  type  of  projection  lantern  (Fig.  543) 
the  series  of  positive  pictures  is  thrown  on  the  screen  at  the  same  rate 
of  speed  as  that  at  which  they  were  taken.  The  sensation  produced 
by  one  picture  remains  until  the  next  picture  appears,  so  that  we 
are  not  aware  of  any  interruption  between  the  pictures.  Thus  we  see 
not  moving  pictures  but  a  rapid  succession  of  stationary  pictures. 

476.  The  simple  microscope,  or  magnifying  glass.  We 
have  said,  in  section  471,  that  the  distance  of  most  distinct 
vision  is  about  10  inches.  If  an  object  is  placed  at  a  greater 
distance  than  this,  the  image  on  the  retina  is  smaller  and  the 
details  of  the  object  are  not  seen  so  distinctly.  If  the  object 
is  placed  nearer  than  this,  the  image  on  the  retina  is  blurred. 

By  placing  the  eye  near  a  double  convex  lens,  often  called  a 
magnifying  glass,  and  placing  the  object  to  be  examined  on 


COMPOUND  MICROSCOPE 


509 


the  other  side  a  little  nearer  the  lens  than  the  principal  focus, 
we  see  a  magnified,  erect  image,  as  shown  in  figure  544.  The 
object-distance  is  adjusted 
until  a  clear  image  is  formed  ; 
then  the  image-distance  is  usu- 
ally about  10  inches.  The 
magnifying  power  of  a  simple 
microscope  is  the  ratio  of  the  ^ , 


Fig.  544.   Diagram  of  a  magnifying  glass. 


size  of  the  image  to  the  size  of 

the  object.     This  is  equal  to 

the  distance  of  the  image  divided  by  the  distance  of  the  object, 

that  is,  10/Do,  D0  being  the  distance  of  the  object  (in  inches) 

from  the  lens. 

Thus  if  for  distinct  vision  a  magnifying  glass  is  held  1  inch 
from  an  insect,  the  magnification  will  be  10  diameters. 

477.   Compound  microscope.     Very  small  objects  are  made 
visible  by  the  compound  microscope.     It  consists  of  two  lenses 


Fig-  545-     A  compound  microscope,  and  a  diagram  of  its  optical  parts. 


510 


LENSES  AND  OPTICAL  INSTRUMENTS 


or  lens  systems  which  are  placed  at  the  ends  of  a  tube.  The 
object  A B  is  put  just  outside  the  principal  focus  of  the  smaller 
lens  L  (Fig.  545),  called  the  objective,  which  forms  an  enlarged, 
real  image  CD.  This  real  image  is  then  examined  through  the 
eyepiece  E,  which  acts  like  a  magnifying  glass,  giving  a  still 
larger  virtual  image  at  C'D',  about  10  inches  from  the  eye. 

The  image  CD  is  magnified  as  many  times  as  its  distance  from  the 
lens  L  is  greater  than  the  focal  length  of  that  lens.  Usually  the  distance 
of  CD  from  L  is  about  150  millimeters ;  and  so,  if  the  lens  has  a  focal 
length  of  5  millimeters,  the  image  CD  is  30  times  as  long  as  the  object 
A  B.  If  the  eyepiece  still  further  magnifies  the  image  10  times,  the 
magnifying  power  of  the  combination  is  10  X  30,  or  300  diameters. 
Microscopes  magnifying  as  much  as  2500  diameters  are  sometimes  used. 

We  are  indebted  to  the  microscope  for  many  valuable  dis- 
coveries about  the  structure  and  life  of  plants  and  animals, 
about  the  smallest  living  things,  and  about  the  causes  of  disease. 

478.  The  telescope.  The  telescope  enables  us  to  see  objects 
so  far  away  that  we  could  not  otherwise  distinguish  their  de- 


546.     Astronomical  telescope  and  optical  diagram. 


tails.  The  simpler  sort,  called  the  astronomical  telescope, 
(Fig.  546)  consists  of  two  lenses  or  lens  systems,  the  large 
objective  0  and  the  eyepiece  E.  The  inverted  real  image  7, 
formed  by  the  lens  0,  is  much  smaller  than  the  object,  but  it  is 
brought  so  near  to  the  observer  that  it  can  be  examined  through 


THE  OPERA    GLASS 


511 


the  eyepiece  E,  which  acts  like  a  magnifying  glass.  The  two 
lenses  are  mounted  in  an  eirioiftiM»n  tube  so  that  the  eyepiece 
can  be  drawn  farther  from  the  objective  when  objects  near  at 
hand  are  to  be  examined.  Since  the  magnifying  glass,  or  eye- 
piece, does  not  rein  vert,  the  observer  sees  things  upside  down, 
just  as  he  does  in  a  microscope. 

479.  The  erecting  telescope,  or  spyglass.  This  instrument  (Fig. 
547)  is  like  the  astronomical  telescope  except  that  an  additional  con- 
verging lens  or  lens  system  L  is  introduced  between  the  object  glass  0 
and  the  eyepiece  E.  This  lens  L  inverts  the  image  7,  forming  another 


Fig.  547.    Erecting  telescope,  or  spyglass. 

real  image  at  /' ;  then  this  erect  image  /'  is  magnified  by  the  eyepiece, 
which  forms  an  enlarged,  erect,  virtual  image  I".  In  the  ordinary 
spyglass  the  eyepiece  is  a  combination  of  two  lenses,  which  act  like  a 
single  magnifying  glass.  The  introduction  of  the  erecting  lens  L 
lengthens  the  telescope  tube  considerably. 

Such  telescopes  are  used  in  sighting  long-range  rifles.  The  "  transit " 
and  "level"  used  by  surveyors  consist  of  a  telescope  provided  with 
cross-hairs  stretched  across  the  telescope  tube  in  the  plane  where  the 
image  of  a  distant  object  is  formed  by  the  object  glass. 

480.  The  opera  glass.  The  opera  glass,  shown  in  figure  548, 
is  a  telescope  whose  eyepiece  is  a  diverging,  or  concave,  lens.  Since 
the  eyepiece  has  approximately  the  same  focal  length  as  the  eye  of  the 
observer,  its  effect  is  practically  to  neutralize  the  lens  of  the  eye.  So 
we  may  consider  that  the  object  glass  forms  its  image  directly  on 
the  retina.  The  field  of  view  of  the  opera  glass  is  small,  and  so  it  is 


512 


LENSES  AND  OPTICAL  INSTRUMENTS 


usually  made  to  magnify  only  three  or  four  times.  But  it  has  the 
advantage  of  being  compact  and  giving  an  erect  image.  The  dis- 
tance between  the  two  lenses  is  equal  to  the  difference  of  their  focal 


Fig.  548.     Opera  glass. 


lengths.     Galileo  made  a  telescope  on  this  plan  which  magnified  about 

30  diameters  and  enabled  him  to  make  some  exceedingly  important 

discoveries. 

481.    The  prism  field  glass,  or  binocular.     An  instrument,  called  a 

binocular,   has  come  into  use  in  recent  years  which  has  the  wide 

field  of  view  of  the  spyglass  and  at 
the  same  time  the  compactness  of 
the  opera  glass.  Compactness  is 
obtained  by  causing  the  light  to 
pass  back  and  forth  between  two 
reflecting  prisms,  as  shown  in  fig- 
ure 549.  This  device  enables  the 
focal  length  of  the  object  glass  to  be 
three  times  as  great  as  in  the  or- 
dinary field  glass  for  the  same  length 
of  tube,  and  so  the  magnifying  power 
is  correspondingly  increased. 


Fig.  549.     Prism  binocular. 


Furthermore,  the  reflections  in  the  two  prisms  secure  an  erect  image 
without  the  use  of  the  erecting  lens  of  the  ordinary  terrestrial  telescope ; 
for  one  double  reflection  tips  the  image  right  side  up,  and  the  other 
shifts  right  and  left,  thus  restoring  it  completely  to  its  natural  position. 


QUESTIONS  AND  PROBLEMS 

1.  When  a  camera  is  focused  on  an  automobile  100  yards  away, 
the  plate  is  8  inches  from  the  lens.  How  much  must  the  distance 
between  the  lens  and  the  plate  be  changed  when  the  automobile  is  only 
10  feet  away  ?  Must  the  distance  be  shortened  or  lengthened  ? 


PRACTICAL  EXERCISES  513 

2.  A  5-inch  post  card  is  to  be  projected  on  a  screen  20  feet  away 
from  the  objective,  so  that  the  picture  will  be  5  feet  long.     Find  the 
focal  length  of  the  lens  required. 

3.  A  photographer  with  a  12-inch  lens  (i.e.,  focal  length  =  10") 
wants  to  make  a  full-length  picture  of  a  6-foot  man  standing  10  feet 
from  the  lens.     How  near  the  lens  must  the  plate  be  placed  ? 

4.  How  long  a  plate  must  be  used  in  problem  3  ? 

5.  How  near  to  an  object  must  a  hand  magnifier  of  1.2  inches 
focal  length  be  held  to  magnify  it  6  diameters  ? 

6.  A  magnifying  glass  of  3  centimeters  focal  length  is  held  ,2.7 
•centimeters  from  an  object,     (a)    Where  will  the  image  be  formed? 
(6)    How  much  will  it  be  magnified  ? 

7.  In  a  compound  microscope  the  objective  lens  L  (Fig.  545)  has 
a  focal  length  of  one  inch,  and  the  object  A  B  is  1.1  inches  away.     How 
far  from  the  lens  is  the  image  CD?     How  many  times  is  it  magnified? 
If  the  eyepiece  magnifies  this  image  20  times,  what  is  the  magnifying 
power  of  the  instrument  ? 

8.  What  is  meant  by  a  "fixed  focus"  camera,  and  how  is  such  a 
camera  constructed  ? 

9.  How  does  a  wide-angle  lens  differ  from  a  long-focus  lens  ? 

10.  If  the  picture  formed  on  a  screen  by  a  projection  lantern  is  too 
small,  which  way  must  the  lantern  be  moved  in  order  to  increase  its 
size? 


11.  Spectacles  are  sometimes  made  with  two 
sets  of  lenses  (bifocal).  What  are  the  advan- 
tages and  disadvantages  of  such  lenses  ? 

PRACTICAL  EXERCISES 

1.  The  periscope.      The  essential  parts  of 
one  form  of  periscope  are  shown  in  figure  550. 
Explain  the  function  of  each  part.      Build  a 
simplified  periscope  to  demonstrate  the  prin- 
ciples involved. 

2.  Range  finder.     Find  out  how  this  instru- 
ment enables  the  observer  to  determine  quickly  Fi                Diagram  of 
the   distance    of   an  object.      (Consult  Ferry's  the  essential  parts  of 
General  Physics  —  John  Wiley  and  Sons.)  a  periscope. 


514  LENSES  AND  OPTICAL  INSTRUMENTS 

SUMMARY  OF  PRINCIPLES  IN  CHAPTER  XXI 

Refraction  occurs  when  light  passes  obliquely  from  one  trans- 
parent substance  to  another. 

When  light  enters  a  denser  substance  obliquely,  it  is  bent 
toward  the  perpendicular. 

Inde*  of  refraction  =  sine  of  angle  of  incidence 
sine  of  angle  of  refraction 
speed  of  light  in  air 


speed  of  light  in  other  substance 
Velocity  of  light  =  186,000  miles  per  second 

=  3  X  1010  centimeters  per  second. 

Critical  angle  is  the  angle  in  the  denser  medium  which  must 

not  be  exceeded  if  the  ray  is  to  get  out. 
Prism  bends  light  toward  thick  edge. 
Convex  (thin-edged)  lens  converges  light  inward. 
Concave  (thick-edged)  lens  diverges  light  outward. 
Principal  focus  is  convergence  point  for  rays  parallel  to  axis. 
Lens  formula :  holds  for  both  converging  and  diverging  lenses : 

1 1  =  1 

Object-distance      image-distance      focal  length 

For  convex  lens,  focal  length  is  positive. 

For  concave  lens,  focal  length  is  negative. 

For  real  image,  lens  between  image  and  object,  image- 
distance  is  positive. 

For  virtual  image,  on  same  side  of  lens  as  object,  image- 
distance  is  negative. 

Size  rule :   Holds  for  both  converging  and  diverging  lenses : 

Length  of  image  _  image-distance 
Length  of  object      object-distance* 


QUESTIONS  515 

QUESTIONS 

1.  Which  people  would  be  more  likely  to  be  short-sighted,  those 
who  live  much  out  of  doors  or  those  who  stay  much  indoors  ? 

2.  How  would  you  distinguish  between  a  slightly  concave  and  a 
slightly  convex  spectacle  lens? 

3.  What  are  the  defects  of  a  pinhole  camera  ? 

4.  What  is  the  difference  between  a  refracting  and  a  reflecting 
telescope? 

6.  Prism  glass  is  often  used  for  the  upper  part  of  shop  windows 
and  doors  and  for  windows  facing  on  narrow  courts.  Draw  a  cross 
section  of  a  plate  of  prism  glass  and  explain  its  action. 

6.  Why  is  it  necessary  to  build  powerful  telescopes  very  wide  as 
well  as  very  long  ? 

7.  Why  is  it  best  to  have  your  light  for  writing  or  sewing  come  from 
over  your  left  shoulder  ? 

8.  Explain  how  it  happens  that  the  wheels  of  moving  vehicles  in 
a  motion  picture  sometimes  seem  to  be  rotating  backwards. 

9.  What  part  do  the  condensing  lenses  play  in  the  action  of  a 
stereopticon  ? 


CHAPTER  XXII 


SPECTRA  AND   COLOR 

Prism  spectrum  —  achromatic  lenses  —  spectroscope  — 
types  of  spectra  —  spectrum  analysis  —  Fraunhofer  lines  — 
wave  length  of  light  —  colors  of  objects  —  colors  of  thin  films 
—  infra-red  and  ultra-violet  —  electromagnetic  theory. 

482.   Analysis  of  light  by  prism.     If  we  let  a  beam  of  sunlight  (or 
one  from  an  electric  arc  lamp)  pass  through  a  narrow  slit  into  a  dark  room, 

and  put  a  glass  prism  in  its 
path  (Fig.  551),  the  beam  of 
light  is  refracted.  If  we  put 
a  white  screen  in  the  path  of 
the  refracted  light,  a  band  of 
colors  is  formed.  In  this 
band  are  red,  orange,  yellow, 
green,  blue,  and  violet,  which 
blend  gradually  into  each 
other. 

A  sharper  image  will  be 
formed  if  a  convex  lens  (focal 
length  about  12  inches)  is 
placed  so  as  to  focus  the  slit 


55i 


White  light   decomposed  by   a 
glass  prism. 


on  the  screen,  and  if  the  prism  is  placed  near  the  principal  focus  on 
the  screen  side  of  the  lens. 

The  colored  band,  which  shades  off  gradually  from  red  to 
violet,  is  called  a  spectrum.  This  shows  that  ordinary  white 
light  is  complex  and  contains  different  kinds  of  light.  The 
light  which  is  refracted  least,  the  eye  recognizes  as  red,  and  that 
which  is  refracted  most,  as  violet.  It  will  be  shown  later  that 
the  physical  property  of  light  which  determines  this  difference 
in  refrangibility  is  the  wave  length. 

To  show  that  the  prism  itself  did  not  produce  the  different  colors, 
but  simply  separated  various  kinds  of  light  already  present  in  the  beam 

516 


SPECTROSCOPE 


517 


of  light,  Sir  Isaac  Newton  placed  a  second  prism  in  the  spectrum,  so  that 
only  violet  light  fell  on  it.  He  found  that  the  violet  light  was  again 
refracted,  but  that  there  was  no  further  change  in  color.  He  also  found 
that  when  these  dispersed  colored  lights  were  brought  together  by  a 
converging  lens,  white  light  was  the  result. 

483.  Achromatic  lenses.  When  sunlight  passes  through  an 
ordinary  double  convex  lens  made  of  a  single  piece  of  glass,  the 
light  is  refracted  and  con- 
verges  at 
the  focus. 


a    point     called 

But  the  light  is 
also  dispersed,  just  as  in  a 
prism,  and  the  focus  for  red 
light  (R  in  figure  552)  is  at 
a  greater  distance  from  the  Fig  552  Dispersion  produced  by  a  lens. 

lens  than  that  for  violet  light  V.  Such  a  single  lens  cannot 
give  a  sharp  image  of  an  object  illuminated  by  ordinary  white 
light,  for  all  the  lines  of  separation  between  light  and  dark 
portions  of  the  image  will  be  colored. 

This  defect,  which  is  known  as  chromatic  aberration,  may  be 
remedied  by  combining  a  lens  of  crown  glass  with  a  lens  of 

flint  glass,  as  shown  in  figure  553. 
By  carefully  designing  the  two  com- 
ponent lenses,  it  is  possible  to  make 
achromatic  lenses,  which  produce 
the  necessary  refraction  without  dis- 
persion. 

484.  Spectroscope.  In  the  spec- 
trum produced  by  a  prism  the  dif- 
ferent colors  overlap  each  other  to 
some  extent.  This  can  be  remedied  by  using  a  spectroscope. 
There  are  four  main  parts  in  a  spectroscope  (Fig.  554) :  the 
collimator,  which  has  a  slit  at  one  end  and  a  convex  lens  at  the 
other  ;  a  prism  commonly  of  flint  glass  ;  a  telescope,  which  has 
an  object  glass  and  eyepiece ;  and  a  scale  tube,  which  has  a 
ruled  scale  at  one  end  and  a  lens  at  the  other.  The  slit  in  the 


Converging      Diver  g  ing 
Fig.  553.     Achromatic  lenses. 


518 


SPECTRA   AND   COLOR 


collimator  is  at  the  principal  focus  of  the  lens  ;  and  so  light  di- 
verging from  the  slit  is  made  parallel  by  the  lens  before  it 
reaches  the  prism.  Here  it  is  refracted  and  dispersed,  each 
color  going  off  as  a  parallel  beam  in  its  own  'direction.  The 


Se 


A'' 


Fig-  554-     Bunsen  spectroscope  with  diagram. 

telescope  forms  a  sharply  defined  image  of  the  spectrum.  The 
scale  tube,  which  is  added  to  locate  the  parts  of  the  spectrum, 
is  so  mounted  that  the  light  from  the  illuminated  scale  is  re- 
flected from  the  second  face  of  the  prism  into  the  telescope 
along  with  the  spectrum. 

485.  Kinds  of  spectra.  The  spectrum  of  sunlight,  or  solar 
spectrum,  is  frequently  seen  after  a  shower  in  summer  time  in 
the  form  of  a  rainbow.  The  sunlight  is  refracted  and  dispersed 
by  the  raindrops.  When  the  solar  spectrum  is  studied  minutely 
with  a  spectroscope,  it  is  found  not  to  be  a  continuous  band  of 
colors,  but  to  be  crossed  by  many  vertical  dark  lines.  Since 
these  lines  were  first  carefully  studied  by  a  German  astronomer, 
Fraunhofer,  they  are  known  as  Fraunhofer  lines. 

Not  all  sources  of  white  light  give  these  dark  lines.  For 
example,  an  electric  arc  lamp,  an  incandescent  lamp  with  a 
tungsten  filament,  an  ordinary  gas  flame,  which  contains  many 


Uinjpodg          cj 


SPECTRUM  ANALYSIS  519 

particles  of  incandescent  solid  carbon   (soot),  and  indeed  all 
incandescent  solids  give  continuous  spectra. 

The  spectrum  of  an  incandescent  vapor  or  gas  is  quite  different. 
It  is  a  bright-line  spectrum,  and  is  characteristic  of  the  substance 
used.  (See  SPECTRUM  CHART  on  the  opposite  page.) 

If  we  dip  a  platinum  wire  or  bit  of  asbestos  into  a  solution  of  common 
salt  (sodium  chloride)  and  hold  it  in  a  blue  Bunsen  flame,  we  get  a 
bright  yellow  flame.  If  we  examine  this  flame  with  a  spectroscope,  we 
see  a  bright  yellow  line,  where  the  yellow  part  of  the  spectrum  would  be. 
This  yellow  light  comes  from  incandescent  sodium  vapor. 

If  we  repeat  the  experiment  with  a  wire  dipped  in  a  chemical  called 
lithium  chloride,  we  get  a  red  flame,  which  gives  in  the  spectroscope 
two  bands,  one  yellow  and  one  red.  Calcium  chloride  also  gives  two 
bands,  green  and  red.  (The  yellow  band,  which  is  likely  to  be  seen 
also,  is  due  to  sodium  present  as  an  impurity.) 

486.  Spectrum  analysis.     When  the   spectroscope  is  used 
to  examine  the  spectrum  of  various  gaseous  substances,  it  is 
found  that  each  element  has  its  own  characteristic  bright-line 
spectrum.     It  may  be  simple,  as  in  the  case  of  sodium;   or  it 
may  be  complex,  as  in  the  case  of  iron  vapor,  which  has  more 
than  four  hundred  lines.     Since  a  very  small   quantity  of  a 
substance  will  show  its  characteristic  spectrum  lines  (less  than 
one  millionth  of  a  milligram  of  sodium  can  be  detected),  we 
have  a  very  delicate  method  of  analyzing  substances.     Spec- 
trum analysis  was  first  used  by  the  chemist  Bunsen  in  1859. 

487.  Absorption   spectra.     Kirchhoff   (1824-1887),    while   a 
professor   of   physics   at  Heidelberg,   worked   conjointly  with 
Bunsen  in  these  investigations  with,  the  spectroscope.     Kirch- 
hoff observed  that  when  he  held  an  alcohol  flame  colored  with 
common  salt  in  front  of  the  slit  of  the  spectroscope  and  allowed 
a  beam  of  sunlight  to  pass  through  the  slit,  the  sodium  line  be- 
came especially  dark  and  sharp,  although  he  had  expected  it 
to  be  especially  bright.     Evidently,  the  sunlight  had  been  in 
part  absorbed  by  the  yellow  sodium  flame  and  the  special  part 
which  the  sodium  flame  itself  ordinarily  gives  out  had  been 
removed.     Kirchhoff  concluded  that,  in  general : 


520 


SPECTRA   AND  COLOR 


A  glowing  gas  absorbs  from  the  rays  of  a  hot  light-source  those 
rays  which  it  itself  sends  forth. 

A   demonstration   of   Kirchhoff's   law    may    be   conveniently    per- 
formed with  the  apparatus  shown  in  figure  555.     The  source  of  light 


Sc 


Fig.  555.     Absorption  of  yellow  light  by  sodium  vapor. 

L  is  the  glowing  positive  carbon  of  the  electric  arc,  whose  rays  are  made 
parallel  by  a  lens  O.  Two  strips  of  asbestos  board,  soaked  in  salt 
water,  are  heated  by  a  wing-top  Bunsen  burner.  The  light  from  the 
electric  arc  passes  directly  through  the  sodium  flame  into  a  "  direct- 
vision  "  spectroscope,  which  disperses  the  light  on  the  screen  Sc. 

First  we  set  the  sodium-flame  burner  to  one  side,  and  produce  a  con- 
tinuous spectrum  on  the  screen.  Then  we  bring  the  sodium  flame  into 
position,  and  we  see  in  the  yellow  portion  of  the  spectrum  a  dark  line. 

If  we  cover  the  lens  0  with  an  opaque  cardboard,  the  spectrum 
disappears,  but  in  the  place  of  the  dark  line  we  now  have  the  bright 
sodium  line.  Or,  if  we  place  a  small  white  screen  with  a  narrow  slit 
where  the  dark  line  is  located  just  in  front  of  the  screen  Sc,  the  dark 
line  on  the  screen  Sc  appears  as  a  yellow  line.  This  shows  that  the  dark 
absorption  band  is  not  absolutely  black,  but  is  so  much  less  intense 
than  the  direct  radiation  from  the  arc  that  it  appears  black  by  contrast. 

It  is  evident,  then,  that  to  produce  dark  absorption  lines  the 
absorbing  vapor  must  be  colder  than  the  luminous  source. 

488.  Meaning  of  Fraunhofer  lines.  We  have  said  in  sec- 
tion 485  that  the  solar  spectrum  contains  a  large  number  of 
dark  lines.  Kirchhoff  concluded  that  these  dark  lines  were 
caused  by  the  presence  in  the  glowing  solar  atmosphere  of 
those  substances  which  themselves  produce  bright  lines  in 


FRAUNHOFER   LINES  521 

the  same  positions.  The  core  of  the  sun  is  at  a  very  high 
temperature  and  gives  forth  a  continuous  spectrum.  But 
this  core  is  surrounded  by  a  layer  of  gas  which  is  cooler  and 
absorbs  those  light  rays  which  it  itself  would  send  out.  On  this 
basis  he  concluded  that  such  metals  as  iron,  magnesium,  copper, 
zinc,  and  nickel  exist  as  vapors  in  the  solar  atmosphere.  After 
much  study  he  found  that  the  bright-line  spectra  of  all  the 
elements  on  the  earth  correspond  in  position  to  certain 
Fraunhofer  lines,  and  concluded  that  all  the  elements  found 
on  the  earth  exist  in  the  atmosphere  of  the  sun.  There  were 
certain  other  Fraunhofer  lines  whose  elements  were  not 
known  on  the  earth  in  KirchhofFs  time.  One  of  these  new 
elements,  helium,  has  since  been  found  on  the  earth,  and  per- 
haps the  others  also  will  sometime  be  found. 

KirchhofFs  explanation  of  the  Fraunhofer  lines  was  epoch- 
making.  Helmholtz  said,  "  It  has  excited  the  admiration  and 
stimulated  the  fancy  of  men  as  hardly  any  other  discovery  has 
done,  because  it  has  permitted  an  insight  into  worlds  that 
seemed  forever  veiled  to  us." 

489.  The  nature  of  light.     We  have  said  that  light  is  con- 
sidered to  be  a  vibration  of  the  ether.     That  is,  light  and  heat 
are  both  forms  of  radiant  energy.     But  we  must  not  think 
that  this  has  always  been  the  accepted  theory.     To  be  sure, 
in  the  seventeenth  century  the  great  Dutch  physicist,  Huygens, 
worked  out  the  wave  theory  very  completely ;    but  his  rival, 
Sir  Isaac  Newton,  in  England,  maintained  the  older  corpuscular 
theory,  according  to  which  light  consists  of  streams  of  very 
minute  particles,  or  corpuscles,  projected  with  enormous  veloc- 
ity from  all  luminous  bodies.     Newton's  reputation  as  a  scien- 
tist was  so  great  that  his  unfortunate  corpuscular  theory  con- 
trolled scientific  thought  for  more  than  a  hundred  years ;  and 
it  was  not  until  the  beginning  of  the  nineteenth  century  that  the 
experiments  of  Thomas  Young  in  England  and  of  Fresnel  in 
France  established  the  wave  theory  on  a  firm  basis. 

490.  Different  colors  due  to  different  wave  lengths.     It  is 


522  SPECTRA   AND   COLOR 

now  possible  to  measure  directly  the  length  of  the  waves  of 
light  of  different  colors,  and  to  show  that  the  waves  of  red  light 
are  longest  and  those  of  violet  are  shortest.  So  in  the  dispersion 
of  sunlight  by  a  prism,  it  is  the  long  waves  (red)  which  are 
refracted  least,  and  the  short  waves  (violet)  which  are  refracted 
most.  The  following  table  gives  the  approximate  wave  lengths 
of  some  of  the  colors. 

WAVE  LENGTHS  OF  LIGHT 

Red       .     .     .     0.000068  cm.  Green     .     .     .     0.000052  cm. 

Orange .     .     .     0.000065  cm.  Blue       .     .     .     0.000046  cm. 

Yellow  ...     0.000058  cm.  Violet     .     .     .     0.000040  cm. 

491.  Colors  of  objects.  The  color  of  any  object  depends 
(1)  on  the  light  which  illuminates  it,  and  (2)  on  the  light  it 
reflects  or  transmits  to  the  eye. 

A  skein  of  red  yarn  held  in  the  red  end  of  the  spectrum  appears  red. 
But  when  held  in  the  blue  end  of  the  spectrum,  it  appears  nearly  black. 
Similarly  a  skein  of  blue  yarn  appears  nearly  black  in  all  parts  of  the 
spectrum  except  the  blue,  where  it  has  its  proper  color. 

Another  striking  experiment  is  to  illuminate  an  assortment  of  bril- 
liantly colored  worsteds  or  paper  flowers  by  the  light  from  a  sodium 
flame.  This  light  contains  only  one  group  of  wave  lengths.  Those 
worsteds  which  reflect  these  particular  wave  lengths  look  yellow,  while 
those  which  do  not  reflect  them  look  dark. 

Thus  it  appears  that  when  a  piece  of  paper  looks  white  in 
daylight,  it  is  because  it  reflects  all  wave  lengths  equally,  and 
when  a  piece  of  cloth  looks  red  in  daylight,  it  is  because  it  re- 
flects only  those  long  waves  which  produce  red  light.  If  the 
white  paper  receives  only  waves  of  red  light,  it  appears  red, 
and  if  the  red  cloth  receives  only  waves  which  have  no  red  in 
them,  it  appears  dark.  That  is,  the  color  of  an  opaque  object 
depends  on  the  wave  length  of  the  light  it  reflects.  The  Cooper- 
Hewitt  mercury- vapor  lamp  is  a  very  efficient  electric  lamp; 
but  it  cannot  be  used  in  places  where  colors  must  be  distin- 
guished, for  it  does  not  furnish  waves  of  red  light. 


MIXING  COLORS  AND   MIXING  PIGMENTS        523 

If  we  place  a  piece  of  red  glass  in  the  path  of  the  light  which  is 
dispersed  by  a  prism  to  form  a  spectrum,  we  see  only  the  red  portion 
of  the  spectrum.  This  shows  that  all  the  wave  lengths  except  the  red 
have  been  absorbed.  In  a  similar  way  a  green  glass  lets  the  green 
light  through,  but  greatly  reduces  the  other  parts  of  the  spectrum.  If  we 
insert  both  the  green  and  the  red  glasses,  the  spectrum  almost  vanishes. 

Thus  we  see  that  the  color  of  a  transparent  object  depends  on 
the  wave  length  of  the  light  it  transmits.  Ordinary  red  glass, 
such  as  photographers  use  for  their  red  lanterns,  transmits 
freely  only  red  light,  and  absorbs  almost  completely  the  yellow, 
green,  blue,  and  violet  light,  which  especially  affect  the  chemical 
compounds  used  on  photographic  plates. 

492.  Mixing  colors  and  mixing  pigments.  There  are  other 
colors  besides  white  which  do  not  have  a  definite  wave  length. 
A  mixture  of  several  wave  lengths  may 
produce  the  same  sensation  as  a  single 
wave  length. 

Let  us  rotate  a  disk  part  red  and  part  green 
(Fig.  556)  so  rapidly  that  the  effect  on  the  eye 
is  the  same  as  though  the  colors  came  to  the 
eye  simultaneously.  The  revolving  disk  ap- 
pears yellow,  much  like  the  yellow  of  the  spec- 
trum. By  mixing  red  and  blue  we  get  purple, 
which  is  not  found  in  the  spectrum.  By  mix- 
ing black  with  red  or  orange  or  yellow  we  get 
the  various  shades  of  brown. 

The  colors  of   the   spectrum  are  called 
pure  colors  and  the  others  compound  col- 
ors.    If  yellow  light  is  mixed  with  just  the 
right  tint  of  blue,  white  light  is  produced.   Fig.  556.  Newton's  color 
Such  colors  are  called  complementary  colors.  disk 

Let  us  pulverize  a  piece  of  yellow  crayon  and  a  piece  of  blue  crayon. 
If  we  mix  the  two  together  about  half  and  half,  the  color  of  the  result- 
ing mixture  is  bright  green. 

This  shows  that  while  mixing  yellow  ana  blue  light  pro- 
duces white,  mixing  yellow  and  blue  pigments  produces  green. 
This  is  because  the  yellow  pigment  absorbs  or  subtracts  from 


524 


SPECTRA   AND   COLOR 


Fig.  557- 

by  the 
film  of 
for  the 


white  light  all  except  yellow 
and  green,  and  the  blue  pig- 
ment subtracts  all  except  blue 
and  green;  therefore  the  only 
color  not  absorbed  by  one  pig- 
ment or  the  other  is  green.  In 
other  words,  in  mixing  pig- 
ments,  the  color  of  the  mixture 
is  that  which  escapes  absorption 
by  the  different  ingredients. 

493.  Colors  of  thin  films. 
The  brilliant  colors  produced 
reflection  of  light  from  thin  transparent  films,  like  the 
a  soap  bubble,  furnish  one  of  the  strongest  arguments 
wave  theory  of  light. 


Interference  of  sodium  light 
waves. 


Let  us  bind  two  pieces  of  plate  glass  A  and  B  (Fig.  557)  together 
with  rubber  bands,  in  such  a  way  that  they 
will  be  separated  at  one  end  by  a  piece  of 
tissue  paper  C.  If  we  hold  the  glass  strips 
behind  a  sodium  flame,  we  see  in  the  reflected 
image  of  the  yellow  flame  a  series  of  fine 
horizontal  dark  lines. 

To  explain  this  effect  we  draw  a 
much-enlarged  section  of  the  glass  plates 
with  the  wedge  of  air  between.  In 
figure  558  let  AB  and  BC  be  the  glass 
plates,  and  let  the  yellow  sodium  light 
be  coming  from  the  right  as  a  series  of 
transverse  waves,  which  we  can  repre- 
sent by  the  wavy  lines.  We  know  that 
this  light  is  in  part  transmitted  and 
in  part  reflected  at  each  glass  surface. 
But  we  are  interested  only  in  what 
happens  at  the  interior  faces  AB  and  Fig  5s8  Explanation  of 

T>n     f  j-u        ix  T~I  it     r   11  i-        ^T-r       formation    of    bright    and 

BC  of  the  plates.     Let  the  full  line  DE      dark  lines 


SUNLIGHT   DECOMPOSED   BY  INTERFERENCE        525 


represent  the  light  reflected  at  the  point  D  on  the  surface  AB, 
and  let  the  dotted  line  D'E  represent  the  wave  reflected  at  D' 
on  the  surface  BC.  If  the  distance  from  D  to  D7  is  such  as 
to  make  one  reflected  wave  just  half  a  vibration  behind  the 
other  in  phase,  they  will  interfere  and  neutralize  each  other. 
At  this  point  we  have  a  dark  line.  But  at  another  point  F  the 
distance  between  the  plates  may  be  such  that  the  wave  reflected 
at  F'  coincides  with  and  reenforces  the  wave  reflected  at  F.  At 
this  point  we  see  a  bright  yellow  line.  If  we  select  any  two 
consecutive  dark  lines,  we  know  that  the  double  path  between 
the  plates  at  one  line  must  be  just  one  wave  length  longer 
than  that  at  the  other  line.  This  gives  us  a  method  of  com- 
puting the  length  of  a  wave. 

FOR  EXAMPLE,  suppose  the  length  of  the  air  wedge  is  100  millimeters, 
the  thickness  of  the  paper  is,0.03  millimeters,  and  the  distance  between 
adjacent  dark  lines  with  sodium  light  is  1  millimeter.  Since  the  width 
of  the  wedge  increases  0.03  millimeters  in  a  distance  of  100  millimeters, 
it  increases  0.0003  millimeters  in  1  millimeter,  and  the  increase  in 
the  double  path  between  adjacent  dark  lines  would  be  0.0006  milli- 
meters. This  is  approxi- 
mately the  wave  length  of 
sodium  light. 

494.   Sunlight  decom- 
posed   by    interference. 

us    dip    a    clean    wire 
a    soap   solution 
up     so     that 
vertical.    The 


Let 

ring    into 
and     set    it 
the    film    is 

water  in  the  film  will  run 
down  to  the  lower  edge, 
and  the  film  becomes  wedge- 
shaped.  Let  a  beam  of  sun- 
light, or  the  light  from  a 
projection  lantern,  fall  on 
this  soap  film  and  be  re-  Fig.  559.  Interference  of  white  light  in  soap 
fleeted  on  a  white  screen  film- 

Furthermore,  let  a  convex  lens  be  arranged,  as  in  figure  559,  so  as  to 
produce  a  sharp  image  of  the  film  F  on  the  screen.     We  see  on 


526 


SPECTRA    AND   COLOR 


the  screen  a    series  of  horizontal  bands  of  the  various  colors  of  the 
spectrum. 

The  white  sunlight  is  composed  of  different  colors  and  so  of 
different  wave  lengths.  The  interference  of  the  red  waves  takes 
place  at  one  point,  and  that  of  the  yellow  at  a  different  point. 
Where  there  is  interference  of  the  red  waves,  the  complementary 
color,  a  sort  of  bluish-green,  is  left ;  and  where  there  is  inter- 
ference of  the  yellow  waves,  the  color  complementary  to  yellow, 
namely,  blue,  is  produced.  Thus  we  have  a  series  of  colored 
bands  which  are  complementary  to  all  the  colors  of  the  spectrum. 

Many  beautiful  color  effects  are  caused  by  the  interference 
of  light  waves  in  very  thin  films.  The  colors  of  oil  films  on 
the  surface  of  water,  of  the  thin  films  of  oxide  on  metals  and  on 
Venetian  glass,  of  the  feathers  of  the  peacock,  and  of  changeable 
silk  are  due  to  the  interference  of  light  waves. 


s 

s 

I 

S//////////////////S7A 

1 

Ultra 
Violet 

$ 

Infra-red 

Electric 
Waves 

\ 

\    1    ii        1 

0. 

1         2       S         456         I?        a        9       10  1    11 
H                           lp                           10ft                           lOOp 

-'-'        13       14      15       16         17  Octal 
imm                     icm.  Wav* 

Fig.  560.     Distribution  of  waves  of  varying  lengths. 

495.  Infra-red  and  ultra-violet  rays.     By  means  of  sensitive 
heat-absorbing  instruments  we  have  come  to  know  that  the  sun 
is  sending  out  not  only  the  light  waves  which  affect  the  optic 
nerve,  but  also  other  longer  ether  waves  which,  though  in- 
visible, yet  can  produce  strong  heating  effects.     They  are  called 
infra-red  rays  (Fig.  560).     We  have  also  learned,  by  photo- 
graphing the  spectrum  of  the  sun,  that  it  is  sending  out  rays 
too  short  to  be  seen,  which  affect  a  photographic  plate,  and 
are  called  ultra-violet  rays. 

496.  Electromagnetic  theory   of  light.     As  we  have   seen, 
Faraday  was  led  to  believe  that  his  "  lines  of  force  "  transmitted 


SUMMARY  527 

electricity  and  magnetism  through  some  medium,  called  the 
ether.  A  few  years  later  Maxwell  developed  this  theory  of 
Faraday's  and  put  it  on  a  mathematical  basis.  The  theory 
was  finally  confirmed  in  1888  by  a  young  German,  Hertz.  His 
experiments  proved  that  electric  waves  really  exist,  and  have 
the  same  velocity  as  light,  although  they  are  sometimes  many 
meters  long.  These  electromagnetic  waves  are  reflected  and 
refracted  like  light  waves.  Therefore,  we  feel  sure  that  light 
waves  are  electric  waves.  This  conception,  and  that  of  the 
conservation  of  energy,  are  the  most  remarkable  achievements 
of  physics  in  the  nineteenth  century. 

SUMMARY  OF  PRINCIPLES  IN  CHAPTER  XXII 

White  light  is  a  mixture  of  a  vast  number  of  waves  of  different 

lengths. 
Difference  in  color  corresponds  to   difference  in  wave  length, 

the  red  waves  being  longer  than  the  violet. 
Wave  length  of  visible  spectrum  ranges  from  about  0.000068 

centimeters  (red)  to  about  0.000040  centimeters  (violet). 
Short  waves  are  most  refracted  by  prisms  and  lenses. 

Continuous  spectrum  formed  by  incandescent  solids. 
Bright-line  spectrum  formed  by  incandescent  gases. 
Dark-line  spectrum  formed  by  incandescent  solid  shining 

through  an  absorbing  layer  of  cooler  gas. 
Color  of  an  object  depends  on  wave  lengths  reaching  eye. 
Colors  of  thin  films  due  to  disappearance  of  certain  wave  lengths 

by  interference. 

QUESTIONS 

1.  A  clean  platinum  wire  is  held  in  a  blue  Bunsen  flame  and  ob- 
served through  a  spectroscope.     What  sort  of  spectrum  is  formed  ? 

2.  What  kind  of  Fraunhof er  lines  does  one  get  in  moonlight  ? 

3.  Why  are  "color  niters"  used  in  photography? 

4.  What  causes  the  various  colored  lights  in  fireworks  ? 


528 


SPECTRA   AND  COLOR 


6.    Why  does  a  blue  dress  look  black  by  the  light  of  a  kerosene 
lamp? 

6.  Why  does  a  reddish  lampshade  make  a  room  seem  more  cheerful 
at  night? 

7.  How  are  colored  motion  pictures  produced  ? 

8.  Why  are  glass  lenses  not  used  in  the  ultra-violet  microscope  ? 

9.  The  only  light  used  in  a  photographic  dark  room  passes  through 
a  red  window.     Explain. 

10.  Explain  why  the  complementary  of  any  one  of  the  spectrum 
colors  is  a  complex  tint  and  not  a  pure  color. 

11.  Explain  why  the  colored  bands  produced  by  the  interference 
of  white  light  by  a  soap  film  are  complex  tints  and  not  pure  spectrum 
colors. 

PRACTICAL  EXERCISES 

1.  Printing  in  colors.     Examine  under  a  magnifying  glass  a  colored 
picture  post  card.     Find  out  how  ordinary  black  and  white  half-tones 
are  made  and  how  the   three-color   half-tones   are  produced.     Get 
sample  prints  from  some  large  printing  establishment  to  illustrate  the 
various  stages  in  the  process. 

2.  Color  blindness.    Test  yourself  and  your  friends  for  color  blind- 
ness by  the  use  of  Holmgren's  Test  Wools.     Find  out  what  the  modern 
theory  is  as  to  the  cause  of  this  defect.     In  what  occupations  would 
this  defect  prove  a  serious  handicap? 

3.  The  colors  of  the  rainbow.    Consult  larger  books  in  physics,  such 

as  KimbalVs  College 
Physics,  for  the  explana- 
tion of  the  colors  of  the 
rainbow.  Make  a  min- 
iature rainbow  on  a 
screen  by  holding  a  glass 
bulb  (about  1  £  or  2  inches 
in  diameter)  filled  with 
water  in  the  path  of  a 
beam  of  sunlight  (or  of 
an  arc  light)  in  a  dark- 
ened room  (Fig.  561). 
Fig.  561.  Making  a  miniature  rainbow.  Explain  the  colors. 


CHAPTER  XXIII 

ELECTRIC   WAVES:  ROENTGEN   RAYS  AND 
RADIOACTIVITY 

Discharge  of  condenser  is  oscillatory  —  electric  resonance  — 
electric  waves  —  detectors  —  radio  telegraphy  and  telephony. 

Discharge  through  gases  —  cathode  rays  —  Roentgen  rays. 

Radioactivity  —  radium  —  its  radiations  —  disintegration 
—  uses  —  energy  changes. 

ELECTRIC  WAVES 

497.  Discharge  of  Leyden  jar  is  oscillatory.  In  1842  Joseph 
Henry  discovered  that  when  a  Leyden  jar  was  discharged 
through  a  coil  of  wire  surrounding  a  steel  needle,  the  needle 
was  magnetized.  Not  only  that,  but  he  was  astonished  to  find 
that  sometimes  one  end  was  made  the  north  pole  and  sometimes 
the  other,  even  though  the  jar  was 
always  charged  the  same  way.  He 
accounted  for  this  fact  by  sup- 
posing that  the  discharge  current 
kept  reversing  back  and  forth, 
that  these  oscillations  gradually 
died  away,  and  that  the  direction 
in  which  the  needle  was  magnet-  Fis-  562.  Curve  of  oscillatory 

,     ,  ,    ,  ,  .  ,  ,.  electric  discharge. 

ized  depended  on  which  way  the 

last  perceptible  oscillation   happened  to  go.     This  oscillatory 

current  is  represented  by  the  curve  in  figure  562. 

A  few  years  later  Lord  Kelvin,  the  great  English  physicist 
and  electrical  engineer,  proved  mathematically  that  the  dis- 
charge must  be  oscillatory.  Finally,  in  1859,  Feddersen  suc- 
ceeded in  photographing  an  electric  spark  by  means  of  a  rapidly 
rotating  mirror.  Figure  563  shows  such  a  photograph.  The 
oscillatory  discharge  is  drawn  out  into  a  band  by  the  rotating 

529 


530 


ELECTRIC   WAVES 


mirror,  and  thus  makes  a  zigzag  trace  on  the  camera  plate. 

From  this  experiment  it  is  possible  to  calculate  the  time  of 
one  oscillation.  It  is  exceedingly  short,  varying 
from  one  one-thousandth  to  one  ten-millionth  of 
a  second. 

498.  Electrical  resonance.  We  have  already 
seen,  in  studying  sound  waves,  that  two  objects 
having  the  same  vibration  frequency  tend  to  vi- 
brate in  sympathy,  and  that  this  property  of 
vibrating  bodies  is  called  resonance. 

Let  us  stretch  a  piece  of  rubber  tubing  between  two 
supports  and  suspend  two  weights  x  and  y  by  threads 
of  equal  length,  as  shown  in  figure  564.  If  we  set  one 
Fig-  563.  pendulum  y  swinging,  the  other  pendulum  x  soon  begins 
Photograph  to  swing,  and  the  first  one  dies  down  as  energy  flows  across 
t i o ns^f  to  the  other-  This  w111  happen  only  if  the  pendulums 
electric  are  °f  the  same  length  and  so  of  the  same  frequency, 
spark.  That  is,  resonance  is  necessary  for  the  transfer  of  energy. 


Now,  the  frequency  of  the  oscillatory  current  produced  by 
discharging  a  condenser  depends  upon  the  capacity  of  the 
condenser,  and  on  the  resistance  and  inductance  of  the  circuit 
through  which  the  current  surges.  Therefore,  if  two  Leyden- 
jar  circuits  have  the  same  capacity,  the  same 
self-induction,  and  the  same  resistance  they 
will  have  the  same  frequency,  and  one  circuit 
will  influence  the  other. 


Let  two  Ley  den  jars  A  and  B  (Fig.  565)  be  of 
the  same  size  and  thickness  of  wall.  To  the  jar  A 
is  connected  a  rectangular  circuit  of  thick  wire, 
one  end  of  which  touches  the  outer  coating  of  the 
jar,  while  the  other  is  separated  from  the  knob  of 
the  jar  by  a  small  spark  gap.  The  jar  B  is  con- 
nected to  a  similar  circuit,  except  that  the  end 
CD  of  the  rectangle  can  be  slid  back  and  forth, 
and  there  is  no  spark  gap.  Finally,  let  the  inner 


Fig.  564.    Resonance 
in  two  pendulums. 


ELECTRIC  RESONANCE 


531 


coating  of  B  be  connected  to  its 
outer  coating  by  a  strip  of  foil  cut 
sharply  across  at  X. 

If  we  place  the  two  electrical 
circuits  a  foot  apart  and  parallel, 
and  send  sparks  across  the  gap  of 
A  by  means  of  an  induction  coil, 
we  find  that  there  is  a  position  of  the 
slider  CD  such  that  tiny  sparks  ap- 
pear at  the  gap  X  in  the  foil  strip 
on  B.  When  the  slider  is  moved 
a  short  distance  from  this  position 
either  way,  the  sparks  at  X  cease. 


Fig 


Resonance     between 
electrical  circuits. 


two 


This   phenomenon   is   called    electric   resonance.     Although 
there  is  no  connection  between  the  two  circuits,  yet  the  energy 

in  one  circuit  surges  over 
into  the  other,  which  is  in 
tune  with  it,  and  causes  a 
spark  there.  In  explanation 
of  this  experiment,  and 
many  others,  we  assume 
that  an  oscillatory  discharge 
or  spark  sends  out  waves  in 
the  surrounding  ether.  The 
ether  does  for  the  electric 
circuits  what  the  rubber  tub- 
ing did  for  the  pendulums. 
It  serves  as  a  medium  for 
the  transfer  of  energy. 

These  electric  waves  were 
first  detected  and  measured 
by  Heinrich  Hertz  (Fig.  566) , 
in  1888,  and  are  therefore 
called  Hertzian  waves. 
Fig.  566.  Heinrich  Rudolf  Hertz  (1857-  They  travel  with  the  same 

1894).     Discovered  the   electromagnetic 

waves  predicted  by  Maxwell.  Velocity  as  light. 


532 


ELECTRIC   WAVES 


499.  Electric-wave  detectors.  The  microphone,  described  in 
section  362,  is  an  excellent  wave  detector.  Another  form, 
called  a  crystal  detector  (Fig.  567),  consists  of  a  piece  of  silicon, 
or  of  any  one  of  several  crystalline  substances,  such  as  galena, 
embedded  in  soft  metal  on  one  side  and  touched  on  the  other  by 
a  metal  point.  The  operation  of  the  crystal  detector  seems  to 
depend  on  some  mysterious  property 
whereby  it  lets  electricity  flow  through 
it  in  one  direction  much  more  easily 
than  in  the  other ;  in  short,  it  acts  as 
a  rectifier. 

A  more  recent  and  far  more  sensitive 
Fig.  567-  crystal  detector,  detector  is  the  vacuum-tube  detector. 
This  works  on  essentially  the  same  principle  as  the  vacuum- 
tube  rectifier,  which  has  already  been  described  in  section 
384.  In  practice  it  is  now  usually  provided  with  three  elec- 
trodes, —  a  tungsten  filament,  a  plate,  and  in  addition  a  third 
electrode,  called  a  grid,  in  between  the  first  two  electrodes. 
Figure  568  shows  the  external 
appearance  of  one  type  of  vac- 
uum tube,  and  figure  568A  is 
a  diagram  to  explain  its  action. 
The  filament  when  glowing  emits 
electrons.  The  effect  of  the 
third  electrode,  or  grid,  is  like 
that  of  a  shutter  which,  opening 
or  closing,  controls  the  flow  of 
electrons  through  it  from  the 
filament  to  the  plate.  When 
the  grid  is  charged  by  a  feeble 
source  of  alternating  current 
positively  or  negatively  with 
respect  to  the  filament,  the  flow 
of  electrons  is  accelerated  or  T 

Fig.    568.       Three-electrode     vacuum 

retarded.     Thus  a  considerable       tube  •  p  plate  •  G  grid ;  F,  filament. 


RADIO   TELEGRAPHY 


533 


-==•  Ground 


Telephone* 


Fig.  s68A.  Diagram  showing  the  use  of  a  vacuum- 
tube  detector  in  a  receiving  circuit  for  radio  tele- 
graphy and  telephony. 


current  flowing  from  the  plate  to  the  filament  may  be  controlled 
by  an  extremely 
small  amount  of  en- 
ergy used  to  charge 
the  grid.  This  is  the 
principle  of  the  vac- 
uum-tube detectors 
and  of  the  telephone 
amplifiers  used  in 
long-distance  tele- 
phony and  radio 
telephony. 

500.  Radio  tele- 
graphy. Through  the 
efforts  of  the  Italian 

inventor,  Marconi,  and  many  others,  electric  waves  are  now 
being  extensively  used  commercially  in  radio  telegraphy. ' 

A  simple  sending  station,  such  as  Marconi  used  in  his  earliest 
experiments,  is  shown  in  figure  569.  The  essential  part  is  a 
conductor,  called  the  aerial  or  antenna,  extending  to  a  consider- 
able height  above  the  ground.  Powerful  electrical  oscillations 
are  set  up  in  this  conductor  like  the  oscillations  in  the  spark 

discharge  shown  in  figure 
562.  These  send  waves  out 
through  the  ether,  just  as  a 
stick  laid  on  water  and  shak- 
en up  and  down  sends  out 
ripples  over  the  surface  of 
the  water. 

One  way  to  set  up  oscilla- 
tions in  an  aerial  is  to  put  a 
spark  gap  in  it,  and  to  send 
sparks    across    this    gap    by 
Ground  ^^         means   of   an  induction  coil 
Fig.  569.    Simple  sending  station.        fed  by  batteries,  or  by  means 


Aerials 


O  Spark 
O  Gap 


534 


ELECTRIC   WAVES 


Aerials 


of  an  alternator  and  step-up  transformer,  as  shown  in  figure  569. 
The  simplest  kind  of  receiving  station  is  represented  in  figure 
570.  There  is  an  aerial  like  that  at  the  sending  station  except 
that,  instead  of  a  spark  gap,  it  contains  a  detector  of  some  sort. 
In  parallel  with  this  detector  is  a  telephone  receiver.  Every 
time  a  train  of  waves  reaches  such  a  receiving  station,  some 
of  the  energy  is  absorbed  by  the  aerial,  and  electrical  oscilla- 
tions are  set  up  in  it.  These  cannot  get  through  the  telephone 
because  of  its  inductance,  and  so  they  have  to  pass  through 
the  detector.  But  since  a  crystal  detector  lets  more  electricity 

through  one  way  than  the  other,  an 
excess  of  electricity  accumulates  in  the 
antenna.  This  excess  then  discharges 
through  the  telephone,  and  the  dia- 
phragm moves  over  and  back  once. 

Since  this  happens  every  time  a  train 
of  waves  comes  in,  which  is  many 
times  every  second,  the  telephone 
diaphragm  is  kept  vibrating  and  emits 
I  a  steady  musical  note  as  long  as  the 
key  of  the  sending  station  is  closed. 
The  duration  of  this  note  can  be  made 
shorter  or  longer  by  holding  the  send- 
ing key  down  a  shorter  or  a  longer 
time ;  and  so  the  dots  and  dashes 
of  the  International  Morse  code  can 
be  transmitted. 

The  circuits  used  in  commercial  wireless  telegraphy  are,  of 
course,  much  more  complicated  than  these,  because  it  is  neces- 
sary to  "  tune  "  the  sending  and  receiving  stations  accurately 
to  the  same  frequency,  and  to  make  them  insensitive  to  waves 
of  any  other  frequency,  so  that  one  pair  of  stations  may  not 
interfere  with  another.  For  an  explanation  of  commercial  send- 
ing and  receiving  stations,  the  reader  may  consult  any  of  the 
numerous  popular  or  technical  books  on  radio  telegraphy. 


Ground 


Fig.    570. 


Simple 
station. 


receiving 


RADIO   TELEPHONY 


535 


501.  Radio  telephony.  Not  long  after  the  first  successful 
experiments  in  radio  telegraphy,  attempts  were  made  to  trans- 
mit speech  by  means  of  electromagnetic  waves.  Experiments 
seem  to  show  that  undamped  continuous  oscillations  of  very, 
high  frequency  are  necessary  for  radio-telephone  work.  The 
frequency  of  this  alternating  current  must  be  above  the  limit 
of  audibility  and  is  often 
about  100,000  cycles  per 
second.  If  such  a  persis- 
tent series  of  oscillations 
passes  through  a  micro- 
phone transmitter  at  the 
sending  station,  and  if  the 
resistance  of  this  micro- 
phone is  made  to  vary 
by  the  voice,  then  the  se- 
quence of  the  waves  is  , 

.  Fig.  571.     High-frequency  oscillations  modi- 

modmed  in   intensity,  and  fied  for  radio  telephony. 

the  amplitude  of  the  high- 
frequency  waves  varies   in   a   way  which  corresponds  to  the 
voice.     These  variations  persist  in  the  rectified  current  through 
the  telephone  at  the  receiving  station  and  are  heard  as  spoken 
words. 

Perhaps  this  will  be  made  clearer  by  studying  the  diagrams  in  figure 
571.  The  rapid  oscillations  OABCDEF  represent  the  high-frequency 
alternating  current  steadily  supplied  to  the  sending  antenna  when 
no  telephonic  transmission  occurs.  But  when  a  microphone  trans- 
mitter is  put  into  the  sending  circuit,  the  amplitude  of  these  outgoing 
waves  is  altered  according  to  the  diagram  O' A' B'C' D' E'F',  and  the 
diaphragm  of  the  telephone  connected  to  the  receiving  antenna  vibrates 
so  as  to  give  out  the  wave  abode. 

For  both  radio  telegraphy  and  radio  telephony  the  receiving 
circuits  are  identical.  The  main  problem  of  radio  telephony 
has  been  the  production  of  continuous-wave  high-frequency 
oscillations  and  the  modulation  of  these  oscillations  through  the 


536  ELECTRIC   WAVES 

human  voice.  At  the  new  radio  central  station  on  Long  Island, 
which  has  a  transmission  range  that  is  practically  world- wide, 
high-frequency  alternators  are  installed.  For  low-power 
commercial  sets  suitable  for  marine,  land,  or  airplane  service, 
three-electrode  vacuum  tubes  are  used  both  for  generating 
the  high-frequency  oscillations  and  for  modulating  them.  For 
further  details  about  the  theory  and  practical  use  of  vacuum 
tubes  in  radio  telephony,  the  reader  should  consult  some  of  the 
special  books  *  on  radio  communication. 

ELECTRICAL  DISCHARGE  THROUGH  GASES 

502.  Sparking  voltage.  The  voltage  needed  to  make  a 
spark  jump  between  two  knobs  depends  on  several  factors, 
such  as  the  size  of  the  knobs,  the  distance  between  them,  and 

the  atmospheric  pressure.  It 
takes  less  voltage  to  cause 
a  spark  to  jump  between  two 
sharp  points  than  between 
two  round  balls.  Thus,  the 
sparking  voltage  for  two 
sharp  points  1  centimeter 
apart  is  about  7500  volts, 

Fig.  572.     Discharge  in  a  partial  vacuum,     while     that     for     two     round 

balls  1  centimeter  in  diame- 
ter and  1  centimeter  apart  is  about  27,000  volts.  The  sparking 
voltage  between  two  sharp  points  varies  so  nearly  as  the 
distance  that  this  is  a  method  used  to  measure  very  high  volt- 
ages. 

To  show  the  effect  of  atmospheric  pressure,  we  may  connect  a  glass 
tube  2  or  3  feet  long  with  an  induction  coil,  as  shown  in  figure  572.  The 
tube  is  connected  with  a  vacuum  pump  by  a  side  tube.  When  the  coil 
is  first  started,  the  discharge  takes  place  between  x  and  y,  the  terminals 
of  the  coil,  which  are  only  a  few  millimeters  apart ;  but  when  the  air  is 

*  The  Principles  Underlying  Radio  Communication.  —  Radio  Pamphlet 
No.  40 ;  United  States  Government  Printing  Office,  Washington,  D.  C. 


CATHODE  RAYS  537 

pumped  out  of  the  tube,  the  discharge  goes  through  the  long  tube  in- 
stead of  across  the  short  gap  xy.  This  shows  that  the  sparking  voltage 
decreases  when  the  pressure  is  diminished. 

503.  Discharges   in   partial    vacua.     Reducing   the   atmos- 
pheric pressure  between  two  points  makes  it  easier  for   an 
electric  discharge  to  pass,  until  a  certain  point  in  the  exhaus- 
tion is  reached.     Then  it  begins  to  be  more  difficult.     At  the 
very  highest  degree  of  exhaustion  yet  attainable,  it  is  hardly 
possible  to  make  a  spark  pass  through  a  vacuum  tube. 

The  changes  in  the  appearance  of  such  a  tube  as  the  ex- 
haustion proceeds  are  very  interesting.  At  first  the  discharge 
is  along  narrow  flickering  lines,  but  as  the  pressure  is  lowered, 
the  lines  of  the  discharge  widen  out  and  fill  the  whole  tube 
until  it  glows  with  a 
steady  light.  With 
still  higher  exhaustion, 

a  soft,  velvety  glow  Fig  573  Geissler  tube,  made  to  study  spectra 
COVers  the  surface  of  of  hydrogen. 

the  negative  electrode, 

or  cathode,  while  most  of  the  tube  is  filled  with  the  so-called  pos- 
itive column,  which  is  luminous  and  stratified,  and  reaches  to  the 
anode.  The  so-called  Geissler  tubes  (Fig.  573)  are  little  tubes 
of  this  sort  which  are  usually  made  in  fantastic  shapes  and  serve 
as  pretty  toys.  The  color  of  the  light  from  a  Geissler  tube 
depends  on  the  gas  which  is  in  the  tube,  and  on  the  kind  of 
glass  used. 

504.  Cathode   rays.     When   the   exhaustion   of   a   tube   is 
carried  to  a  very  high  degree,  so  that  the  pressure  is  equal  to 
about  0.0001  of  a  millimeter  of  mercury,  the  positive  glow  is 
very  faint  and  the  dark  space  around  the  cathode  is  pervaded 
by  a  discharge.     An  invisible  radiation  streams  out  nearly  at 
right  angles  to  the  cathode  surface,  no  matter  where  the  anode 
is  located  in  the  tube.     This  radiation  from  the  cathode  is 
called  cathode  rays  and  shows  itself  in  several  ways :  first,  by 
a  yellowish  green  fluorescence  wherever  it  strikes  the  glass  of 


538 


ELECTRIC   WAVES 


the  tube  ;  second,  by  the  fact  that  it  can  be  brought  to  a  focus, 
where  it  produces  intense  heat ;  and  third,  by  the  sharply  defined 
shadow  which  a  metal 
interposed  in  its  path 
produces  in  the  fluor- 
escence on  the  end  of 
the  tube. 


Fig    575-     Shadow    formed 
cathode  rays. 


Fig.  574-  Heat- 
ing effect  of 
cathode  rays. 


A  vacuum  tube,  ar- 
ranged as  in  figure  574, 
shows  the  heating  effect 
of  the  cathode  rays. 
When  an  induction  coil 
sends  a  discharge  through 

the  tube  from   top  to  bottom,  the  cathode  rays  are 
focused  on  a  piece  of  platinum,  which  becomes  red  hot. 

Another  vacuum  tube,  arranged  as  in  figure  575, 
shows  that  a  shadow  is  formed  on  the  end  of  the  tube 
by  an  aluminum  cross. 


M 


505.  What  are  cathode  rays?  A  vacuum  tube,  made  as  in 
figure  576,  sends  a  narrow  band  of  cathode  rays  through  the 
slit  s  in  the  aluminum  screen  mr  against  a  fluorescent  screen  / 
slightly  inclined  to  them.  When  a  strong  mragnet  M  is  held 

near  the  side  of  this  tube,  it 
is  found  that  the  stream  of 
cathode  rays  is  deflected  in 
the  direction  which  would 
be  expected  if  they  were  a 
stream  of  negatively  charged 
particles.  From  this  and 
other  experiments  we  be- 


Fig.  576. 


Bending  of  cathode  rays  by  a 
magnet. 


lieve  that  cathode  rays  are 
streams  of  electrons  shot  off 
from  the  surface  of  the  cathode  at  very  high  velocity. 

J.  J.  Thomson,  the  English  physicist,  has  estimated  from 
various  experiments  on  cathode  rays  that  these  electrons  have 
each  a  mass  about  sixteen  hundred  times  smaller  than  that  of  a 


ROENTGEN  RAYS 


539 


X  Rays 

Roentgen,  or  X-ray,  tube. 


hydrogen  atom,  and  move  with  a  velocity  of  from  one  tenth  to 

one  third  that  of  light.     It  is  supposed  that  each  particle  carries 

a  negative   charge   of  electricity 

equal  to   that   of   the  hydrogen 

atom  in  electrolysis. 
506.  Roentgen,    or     X,    rays. 

In     1895,     while     experimenting 

with  a  vacuum  tube,  Roentgen 

discovered  another  kind  of  rays, 

which  he  called  X  rays.     When 

cathode    rays    strike    against    a    Fig 

platinum    target,    as    shown    in 

figure  577,  Roentgen  rays  are  sent  off  from  this  target.     They 

affect  a  photographic  plate  somewhat  as  sunlight  does ;    but, 

like  cathode  rays,  they  will 
penetrate  many  substances 
opaque  to  ordinary  light, 
such  as  wood,  pasteboard, 
and  the  human  body 
That  they  are  not  the  same 
as  cathode  rays  is  shown  by 
the  fact  that  they  are  not 
deflected  by  a  magnet. 

When  a  photographic 
plate,  inclosed  in  the  usual 
plate-holder  with  sides  of 
hard  rubber  or  pasteboard, 
is  exposed,  with  a  hand 
held  over  it,  to  Roentgen 
rays,  a  shadow  picture  like 
that  seen  on  the  fluorescent 
screen  is  formed  (Fig. 
578). 


Fig-  5?8.     Radiograph  of  a  hand. 


We  may  demonstrate  the  action  of  Roentgen  rays  by  operating  an 
X-ray  tube  with  an  induction  coil,  and  holding  a  fluorescent  screen  in 


540  ELECTRIC   WAVES 

front  of  the  bulb.  If  the  room  is  dark  and  the  hand  is  interposed  be- 
tween the  tube  and  the  screen,  the  flesh,  which  is  easily  penetrated  by 
the  rays,  will  be  seen  faintly  outlined,  while  the  bones  will  cast  a 

strong  shadow.     Such  a  radiograph 
of  the  teeth  is  very  valuable   to 
-Anti-cathode1    the  dentist  in  locating  an  abscess 
on  the  root  of  a  tooth. 

Roentgen,    or    X,   rays   are 
produced    at    and    sent   forth 

Fig.  579.     Coolidge  X-ray  tube.         from  anY   solid  body   on   which 

cathode    rays   fall.     They    are 

now  known  to  be  ether  waves,  just  like  light  waves,  but  of 
very  much  shorter  wave  length. 

The  penetrating  power  ("hardness")  of  X  rays  is  increased  by 
diminishing  the  gas  pressure  within  the  tube  and  by  increasing  the 
voltage  across  the  electrodes.  The  Coolidge  X-ray  tube  (Fig.  579)  is 
exhausted  so  completely  that  it  is  impossible  to  send  a  discharge  through 
the  tube.  To  get  the  necessary  electrons,  an  incandescent  cathode  is 
employed.  This  consists  of  a  tungsten  spiral  heated  by  a  subsidiary 
electric  current  from  a  12-volt  storage  battery.  The  tungsten  wire  is 
surrounded  by  a  molybdenum  tube,  which  serves  to  focus,  the  stream 
of  electrons  on  the  anticathode,  which  is  also  made  of  tungsten.  The 
intensity  of  the  X  rays  is  precisely  and  readily  controlled  by  adjusting 
the  temperature  of  the  cathode. 

507.  Radioactivity.     In    1896,    Henri    Becquerel,    in    Paris, 
discovered  that  something  resembling  X  rays  is  radiated  by 
pitch  blende  and  other  minerals  that  contain  the  element  ura- 
nium.    He  found  that  if  a  photographic  plate,  wrapped  in  black 
paper,  is  placed  close  to  one  of  those  minerals,  a  shadow  photo- 
graph of  an  intervening  coin  or  other  dense  object  is  formed. 
This  phenomenon  is  called  radioactivity. 

508.  How  radium  is  obtained.     Soon  after,  M.  and  Mine. 
Curie  (Fig.  580),  also  in  Paris,  found  that  thorium,  which, 
next  to  uranium,  is  the  heaviest   element   known,  possessed 
the  same  property.    They  were,  however,  astonished  to  find  that 
pitch  blende  from  a  certain  locality  in  Austria  showed  more 
radioactivity  than  an  equal  weight  of  either  pure  uranium  or 


RADIUM 


541 


pure  thorium.  It  was  thus  made  evident  that  this  particular 
pitch  blende  contained  some  other  substance  far  more  radioactive 
than  either  uranium  or  thorium.  After  long  months  of  arduous 
work,  Mme.  Curie  succeeded  in  separating  a  minute  quantity 
of  this  new  substance  in  a  fairly  pure  state  from  many  tons 
of  pitch  blende.  It  proved  to  be  a  hitherto  unknown  chemical 
element,  which  she  named 
radium.  It  has  a  radioac- 
tivity a  million  times  that 
of  an  equal  weight  of  the 
pitch  blende  in  which  it  was 
first  found,  and  is  four 
million  times  as  active  as 
pure  uranium. 

Most  of  the  radium  now 
being  produced  in  the  world 
comes  from  a  certain  kind 
of  ore  found  in  Colorado. 
It  takes  500  tons  of  this  ore, 
and  500  tons  of  chemicals 
used  in  treating  it,  to  say 
nothing  of  the  quantities 
of  coal  for  heating  and  of 
water  for  dissolving  and 
washing,  to  produce  a  single 
gram  of  radium,  and  skilled 
men  have  to  put  in  much  work  besides;  so  that  it  is 
no  wonder  that  radium  costs  $100,000  a  gram. 

Radium  is  ordinarily  sold  and  used,  not  in  its  pure  or  metallic 
form,  but  combined  with  bromine  in  the  form  of  a  salt  that 
looks  very  much  like  common  salt.  The  salt  containing  a 
gram  of  radium  weighs  about  1.7  grams. 

509.  Uses  of  radium.  The  radiations  given  off  by  radium 
are  extremely  active.  It  is  possible  with  their  aid  to  take 
pictures  in  exactly  the  same  way  as  with  X  rays.  Radium 


Fig.    580.     Mme.    Curie   at   work  in   her 
Paris  laboratory. 


542  ELECTRIC   WAVES 

rays  exert  a  very  powerful  action  on  living  matter,  and  this  has 
led  to  the  hope  that  they  will  be  useful  in  curing  various  diseases ; 
indeed  in  treating  certain  kinds  of  cancer  and  similar  growths 
radium  seems  to  be  very  beneficial.  Radium,  which  is  ex- 
tremely expensive,  is  continually  producing  radium  emanation, 
and  it  is  the  emanation  instead  of  the  radium  itself  that  is  com- 
monly used  in  treating  diseases.  Every  day  the  emanation  is 
pumped  off  from  the  radium  salt  and  collected  in  very  tiny  glass 
tubes.  These  tubes  are  then  inserted  in  the  flesh  near  the 
cancer.  Their  curative  power  results  from  the  fact  that  these 
rays  kill  diseased  tissue  much  faster  than  they  kill  healthy  tissue. 

Certain  radioactive  elements  in  an  impure  condition  have 
been  used  in  the  manufacture  of  luminescent  paint.  They  are 
mixed  with  zinc  sulfide,  which  fluoresces  when  in  contact  with 
radium  particles.  Luminescent  paint  makes  watch  and  clock 
faces  glow  in  the  dark ;  and  little  buttons  covered  with  it  help 
to  locate  light  switches  or  doorknobs  at  night. 

510.  Energy  of  radium.  One  of  the  most  remarkable  proper- 
ties of  radium  and  its  salts  is  that  they  are  continually  producing 
heat  and  are  generally  three  to  five  degrees  warmer  than  their 
surroundings.  Careful  experiments  show  that  one  gram  of 
radium  gives  off  100  calories  per  hour.  This  evolution  of  heat, 
although  at  a  slow  rate,  continues  for  so  long  a  time  before  a 
gram  of  radium  is  completely  disintegrated,  that  the  total  heat 
which  the  gram  will  produce  in  its  long  life  is  nearly  300,000 
times  as  much  as  a  gram  of  .coal  produces  when  it  is  burned. 

These  facts  are,  in  themselves,  of  no  practical  importance 
from  the  point  of  view  of  the  energy  needed  in  commerce  and 
industry,  because  radium  is  so  rare  and  so  expensive.  They 
make  it  plain,  however,  that  inside  the  atoms  of  all  substances, 
including  coal  itself,  there  must  be  stores  of  potential  energy 
so  vast  in  comparison  with  our  ordinary  heats  of  combustion 
as  to  be  of  overwhelming  importance,  if  we  could  only  learn 
how  to  set  them  free. 

Unfortunately,  however,  even  in  the  case  of  radium,  the 


SUMMARY  543 

rate  at  which  this  energy  is  set  free  has  been  found  to  be  ex- 
actly the  same  at  the  extreme  cold  of  liquid  air  as  at  ordinary 
temperatures,  and  to  be  entirely  unaffected  by  anything  that 
we  can  do  to  the  radium ;  that  is,  it  is  entirely  uncontrollable. 
Who  shall  say,  however,  what  the  future  has  in  store? 


SUMMARY  OF  PRINCIPLES  IN  CHAPTER  XXIII 

Ether  waves  are  set  up  by  an  electric  spark ;  they  were  first  de- 
tected by  Hertz. 

Discharge  of  a  condenser  through  a  circuit  of  small  resistance 
is  oscillatory. 

Two  electric  circuits  so  tuned  as  to  have  the  same  frequency 
are  said  to  be  in  resonance. 

Crystal  detectors  and  vacuum-tube  detectors  act  as  rectifiers. 
The  latter  may  also  act  as  amplifiers. 

In  radio  telegraphy  electric  waves  are  sent  from  an  aerial,  trans- 
mitted through  the  ether,  and  received  by  another  aerial 
connected  with  a  detector  and  telephone. 

In  radio  telephony  undamped  continuous  oscillations  of  very 
high  frequency  are  modified  in  intensity  by  the  varying 
resistance  of  the  transmitter.  Receiving  station  like  that 
used  for  radio  telegraphy. 

Cathode  rays  are  streams  of  negatively  electrified  particles, 
called  electrons,  shot  off  from  the  cathode  surface. 

Roentgen,  or  X,  rays  are  produced  where  cathode  rays  strike  a 
solid  object  or  target.  They  pass  through  glass  and  affect 
a  photographic  plate.  They  penetrate  different  materials 
approximately  inversely  as  the  densities  of  the  materials 
These  rays  are  identical  with  ultra-violet  light  of  extremely 
short  wave  length. 

Radioactive  substances  emit  spontaneously  rays  which  are  similar 
to  X  rays.  Radium  evolves  heat  slowly  but  continuously. 


544  ELECTRIC   WAVES 

QUESTIONS 

1.  What  is  the  relation  between  the  length  and  frequency  of  an 
electric  wave? 

2.  What  evidence  have  we  for  thinking  that  an  electric  spark  starts 
a  series  of  ether  waves  ? 

3.  What  is  the  function  of  the  aerial  wires  used  in  radio  stations  ? 

4.  What  advantages  has  the  International  Morse  code  over  the 
ordinary  Morse  code? 

6.    What  is  the  experimental  evidence  for  believing  that  cathode 
rays  are  negatively  charged  particles,  and  not  ether  waves? 

6.  What  is  the  experimental  evidence  for  believing  that  X  rays 
are  extremely  short  waves,  similar  to  but  shorter  than  the  ultra-violet 
light  rays  ? 

7.  How  is  radioactivity  different  from  the  usual  chemical  action  ? 

8.  How  could  one  test  the  activity  of  a  radioactive  substance? 

PRACTICAL  EXERCISES 

1.  Radio  station.     Set  up  a  telegraph  key  with  a  dry  cell  and  buzzer. 
Learn  the  International  code.     Then  construct  and  operate  a  simple 
receiving  and  sending  apparatus.     Improve  your  outfit  as  you  become 
more  proficient  in  its  use  and  understand  its  working. 

2.  Radioactivity.    Wrap  a  photographic  plate  in  black  paper.    Lay  a 
Welsbach  mantle  on  the  paper  next  to  the  film  side  of  the  plate.     Flat- 
ten it  down  and  leave  the  whole  in  a  light-tight  box  for  a  week.   Then 
develop  the  plate.     A  picture  of  the  mantle  will  appear  on  it. 

3.  Ignition  testers.    A  device  for  testing  the  ignition  system  of  an 
automobile  has  recently  appeared,  which  consists  of  a  hard-rubber  case 
containing  a  glass  tube.     When  the  device  is  held  near  a  spark  plug 
that  is  working  well,  the  glass  tube  glows  with  a  bright  orange  light. 
Find  out  how  such  a  device  is  made  and  how  it  works.     What  is  in  the 
glass  tube?     What  makes  it  glow?     Find  out  how  useful  such  devices 
are  found  to  be  in  practice. 


INDEX 


[References  are  to  pages.] 


Aberration,  chromatic,  517 ;  spherical, 
of  lens,  501,  of  mirror,  476. 

Absolute,  pressure,  121 ;  temperature, 
205;  zero,  206,  210. 

Absorption,  of  gases,  123,  124 ;  spectra, 
519. 

A.  C.,  see  current,  alternating. 

Acceleration,  161  to  173,  table,  162; 
force  causing,  178,  184. 

Accommodation,  504. 

Achromatic  lens,  517. 

Adhesion,  91. 

Aerial,  533. 

Air,  buoyancy  of,  112;  compressibility 
of,  118;  density  of,  96,  120;  elas- 
ticity of,  119;  moisture  in,  246; 
saturated,  247;  under  pressure,  117 
to  123. 

Air-brake,  118; -compressor,  117. 

Airplanes,  142  to  145. 

Airships,  114  to  116. 

Alternating  current,  see  current,  al- 
ternating. 

Alternator,  375,  413  to  416  ;  uses,  420 ; 
high  frequency,  536. 

Altitude  by  barometer.  107. 

Ammeter,  317,  318,  344. 

Ampere,  311,  313  to  315,  360. 

Ampere,  Andre  Marie,  311. 

Amplifier,  532. 

Amplitude,  of  a  wave,  433;  deter- 
mines intensity  of  sound,  443. 

Aneroid  barometer,  105,  106. 

Anode,  357  to  361. 

Antenna,  533. 

Arc,  electric,  353 ;   lamps,  353  to  355. 

Archimedes'  principle,  72  to  75,  113. 

Armature,  of  bell,  341 ;  drum,  379, 
385,  408;  of  generator,  374; 
Gramme-ring,  377 :  of  motor,  383, 
389 ;  stationary,  414. 

Astigmatism,  505. 

Atmosphere,  96;  moisture  in,  246  to 
250 ;  pressure  of,  100,  103,  104,  107  ; 
refraction  in,  489. 


Atom,  304,  539,  543. 

Attraction,  electric,  293,  295;  gravita- 
tional, 182,  183;  magnetic,  281, 
282,  287  ;  molecular,  92. 

Audibility,  limits  of,  443. 

Automatic,  door-closing  spring,  157; 
stoker.  259. 

Automobile,  frontis.,  2,  3;  accelera- 
tion of,  173;  battery,  363,  364; 
brakes,  27,  29,  30,  184;  cam,  42; 
carburetor,  270 ;  center  of  gravity, 
36;  centrifugal  pump,  111;  chains, 
51 ;  clutches,  cone,  51,  multiple  disk, 
52 ;  condenser  in  spark  coil,  306 ; 
cooling  systems,  216,  271 ;  differ- 
ential, 50;  engine,  271  to  275; 
fuel,  268  ;  gasoline  pump,  122  ;  head- 
lights, 478,'  485 ;  horn,  462 ;  igni- 
tion system,  394  to  397 ;  ignition 
tester,  544 ;  induction  coils,  394 ; 
jack,  42,  59;  lubrication,  53;  mag- 
neto, 394,  395  ;  mirror,  478;  muffler, 
272,  462;  permanent  magnets  in, 
289 ;  shock  absorber,  157 ;  skid- 
ding, 51,  176;  spark  plug,  272, 
394  ;  pressure  in  tire,  208  ;  speedom- 
eter, 160;  starter,  383,  392;  tire 
pump,  118;  tire  gauge,  127;  traction, 
51 ;  throttle,  270,  275 ;  trans- 
mission, 280 ;  worm  gear  drive,  44. 

Balance,     platform,     8;      spring,     8; 

-wheel  in  watch,  202. 
Ball  bearings,  56,  58. 
Balloons,  113  to  116. 
Barograph,  105,  106. 
Barometer,  104  to  107 ;   made,  109. 
Battery,     328;      ignition,     396,     397; 

telegraph,  342,  343;  telephone,  399, 

400;    storage,  362  to  367;    also  see 

cell. 

Beats,  451  to  453. 
Bell,   electric,   308,   341;    transformer 

for  ringing,  403,  404,  410. 
Belt,  48. 


545 


546 


INDEX 

[References  are  to  pages.] 


Bending,  150,  152. 

Binocular,  512. 

Biplane,  142. 

Blood  pressure,  122. 

Blower,  111. 

Boiler,  256  to  259;    kitchen  b.,  214. 

Boiling  point,  196,  237  to  239,  table, 
239 ;  effect  of  pressure  on,  237, 
table,  238. 

Bourdon  gauge,  85,  121. 

Boyle's  law,  119,  209. 

Brake,  air,  118  ;  automobile,  27,  29,  30 ; 
for  testing  a  motor,  391. 

Breaking  strength,  154. 

Bridges,  140,  141,  148. 

British  thermal  unit,  226 ;  mechanical 
equivalent  of,  279  ;  electrical  equiv- 
alent of,  350. 

Bunsen  photometer,  466. 

Buoyancy,  of  air,  112;  of  liquids, 
71. 

Calorie,  226 ;  mechanical  equivalent 
of,  279  ;  electrical  equivalent  of,  350. 

Calorimeter  (Parr  bomb),  230. 

Cam,  42. 

Camera,  502. 

Candle  power,  466. 

Capacity,  of  boiler,  256;  electric,  300, 
412  ;  of  storage  cell,  365  ;  volumet- 
ric, 6. 

Capillarity,  92  ;  in  soils,  92. 

Carburetor,  270. 

Cathode,  357  to  361,  537;  incandes- 
cent c.,  540;  c.  rays,  537,  538,  539, 
540. 

Cell,  causes  difference  of  potential,  3Q9 ; 
hydraulic  analogy  of,  310 ;  terminal 
voltage  of,  332;  dry,  330  to  3~32  ; 
sal-ammoniac,  334 ;  simple,  309 : 
storage,  36^to  367  ;  also  see  battery. 

Cells,  best  arrangement  of,  327  to  329. 

Center,  of  curvature,  475  ;  of  gravity,  23. 

Centigrade  scale,  196. 

Centrifugal,  pump,  110;  tendency, 
176  to  178. 

Centripetal  force,  176. 

Charles'  law,  206. 

Circuit,  electric,  310;  partial,  323; 
parallel,  324  to  326;  series,  322; 
telegraph,  342  ;  telephone,  400 ;  wire- 
less, 533,  534. 


Circuit  breaker,  348. 

Clinical  thermometer,  197. 

Clouds,  249,  250. 

Coefficient,  of  expansion,  201  to  205; 
of  friction,  54,  137. 

Cohesion,  91. 

Color,  521  to  526;  -blindness,  528; 
-printing,  528. 

Commutator,  376,  378;    -motor,    421. 

Compass,  282. 

Complementary  colors,  523. 

Component,  of  a  force,  135. 

Composition  of  forces,  130  to  133. 

Compound,  bar,  199  ;  color,  523  ;  en- 
gine, 262  ;  generator,  382  ;  machine, 
45. 

Compressed  air,  117  to  121. 

Compressibility,  of  fluids,  119. 

Compression,  150,  152 ;  c.  members, 
141. 

Compressors,  air,  117. 

Computing  scales,  59. 

Condenser,  electric,  299  to  302,  411 
to  413  ;  steam,  99,  240,  261. 

Conduction,  of  electricity,  294,  305; 
of  heat,  217  to  219;  by  solutions, 
357. 

Conductor,  distribution  of  electricity 
on,  297. 

Conjugate  foci,  of  lens,  498  ;  of  mirror, 
480. 

Conservation  of  energy,  191,  279. 

Controller,  390.  . 

Convection,  211  to  216,  235,  271. 

Coolidge  X-ray  tube,  540. 

Cooker,  fireless,  219  ;  pressure,  239. 

Cooper-Hewitt  lamp,  355. 

Corliss  engine,  260,  261. 

Cornet,  457. 

Coulomb,  311,  314,   360;   -meter,  361. 

Crane,  45,  132,  146. 

Cream  separator,  177. 

Critical  angle,  493. 

Crystal  detector,  532. 

Current,  alternating,  375,  403  to  426, 
535;  chemical  effects  of,  357  to 
366  ;  convection,  211  to  216  ;  direct, 
307  to  369  ;  eddy,  408,  409  ;  heating 
effect  of,  346  to  348  ;  high  frequency, 
535  ;  induced,  370  to  402  ;  magnetic 
effect  of,  337  to  346,  384 ;  measure- 
ment of,  311,  316,  317,  345,  360; 


INDEX 

[References  are  to  pages.] 


547 


power  of,  348  to  350,  411 ;  rectified, 
425 ;  in  revolving  loop,  374 ;  of 
water,  307,  308. 

Curie,  Mme.  M.  S.,  541. 

Curtis  turbine,  267. 

Curvature,  center  of,  475. 

Cycles,  417. 

Dampers,  225. 

Damping,  409. 

Declination,  282. 

D.  C.,  see  current,  direct. 

De  Laval  turbine,  265. 

Density,  9  to  11,  table  10;  of  air,  96, 
120 ;  of  water,  204 ;  vs.  specific 
gravity  77. 

Derrick,  36. 

Detectors,  531,  532. 

Dew,  249;   -point,  248,  249. 

Dielectric,  300. 

Diesel  engine,  276. 

Diffusion,  of  gases,  124 ;   of  light,  472. 

Dip,  283. 

Direct  current,  see  current,  direct. 

Discharge,  of  condenser,  302,  529; 
through  gases,  536  to  540  ;  of  light- 
ning, 303. 

Discord,  453. 

Distillation,  239  ;   fractional,  240. 

Door-closing  spring,  157. 

Draft,  213,  258. 

Drinking  fountain,  127. 

Drum  armature,  379,  385,  408. 

Dry  cell,  330  to  332. 

Dry  dork,  75. 

Dynamo,  see  generator. 

Dyne,  179;  -centimeter,  189. 

Earth,  as  magnet,  284. 

Eccentric,  260. 

Echo,  439. 

Economizer,  2] 4. 

Eddy  currents,  408,  409. 

Edison,  phonograph,  460 ;   cell,  365. 

Efficiency,  defined,  55  ;  of  boiler,  259  ; 
of  Edison  cell,  366;  of  electric 
motor,  390 ;  of  incandescent  lamps, 
353 ;  of  locomotive,  262 ;  of  steam 
plant,  261 ;  of  transformer,  405 ; 
of  water  wheels,  87,  90. 

Elastic  limit,  153,  155. 

Elasticity,  149  to  157. 


Electric,  see  alternator,  ammeter,, 
amplifier,  arc,  armature,  attraction, 
battery,  bell,  capacity,  cell,  cells, 
circuit  circuit  breaker,  commutator, 
condenser,  conduction,  conductor, 
controller,  current,  detectors,  dis- 
charge, eddy  currents,  efficiency, 
electro-,  energy,  flat-iron,  force,  fre- 
quency, fuse,  galvanometer,  genera- 
tor, heating,  ignition  systems, 
impedance,  induc>i6nT  inertia,  insu- 
lators, lamps,  light,  mejter,  motor, 
oscillations,  potential,  power,  pyrom- 
eter, rectifiers,  refining,  repulsion, 
resistance,  resonance,  self-induction, 
sewing  machine,  spark,  telegraph, 
telephone,  thermometer,  transformer, 
transmission,  units,  waves,  welding, 
work. 

Electricity,  2,  293  to  426,  529  to  540 ; 
atmospheric,  302 ;  electron  theory  of, 
304 ;     frictional,    293 ;     a   source   of 
heat,  194 ;     positive    and    negative, 
295 ;     produced   by  induction,   302 ; 
unit  of  quantity  of,  311. 
Electro,  -chemical  equivalents    (table) 
360;    -magnets,  339  to  346;    -mag- 
netic theory  of  light,  526 ;    -plating, 
358  ;   -statics   307  ;   -typing,  359. 
Electrode,  310,  358,  537. 
Electrolysis,  of  water,  357 ;   theory  of, 

358. 

Electrolyte,  310,  357. 
Electrolytic,    cleaning,    361  ;     copper, 

359;  rectifier,  425. 

Electromotive  force  (or  voltage),  312; 
back,  331,  387,  411;  of  cells,  313; 
of  combinations  of  cells,  327,  328 ; 
computed,  323  ;  of  Edison  cell,  366  ; 
,  of  generators,  381,  382;  of  ignition 
circuits,  394,  395;  induced,  371  to 
373;  of  lead  cell,  365;  measured. 
317,  345;  sparking,  536;  terminal, 
332,  333  ;  of  transformers,  403,  404  ; 
of  transmission  lines,  407 ;  in  watt- 
hour  meter,  424. 

Electrons,  295,  304,  305,  425,  538,  540. 
Electrophorus,  302. 
Electroscope,  296. 
E.  m.  f.,  see  electromotive  force. 
Energy,  186  ;   absorbed  by  aerial,  533  ; 
conservation  of,   192,   279;    dissipa- 


548 


INDEX 

[References  are  to  pages.] 


tion  of,  192;  electrical,  349,  353; 
equation,  188,  189 ;  in  generator, 
382 ;  kinetic,  187  to  190 ;  potential, 
186,  187;  radiant,  221,  223  /  of 
radium,  542 ;  of  sound  waves,  437, 
438,  441 ;  in  storage  cell,  362  ;  trans- 
fer of,  530,  531 ;  transformation  of, 
191,  278  ;  in  transformer,  405. 

Engine,  automobile,  frontis.,  3,216,  271 
274 ;  compound,  262 ;  condensing, 
261 ;  Corliss,  260 ;  Diesel,  276 ; 
efficiency  of,  261;  Ford,  275;  4- 
stroke,  272 ;  gas,  268  to  270 ;  gaso- 
line, 270  to  275;  hot-air,  211; 
internal  combustion,  268  to  277 ; 
kerosene,  275 ;  oil,  268,  275  to  277 ; 
quadruple-expansion,  262 ;  slide- 
valve,  260;  solid  injection,  278; 
steam,  255,  260  to  263,  382 ;  triple- 
expansion,  262 ;  2-stroke,  273 ;  uni- 
flow,  262. 

Equilibrant,  131. 

Equilibrium,  conditions  of,  34,  131. 

Erg,  189. 

Escapement  wheel,  173. 

Ether,  220,  287,  490,  521,  527,  531,  533, 
540. 

Evaporation,  246. 

Exciter,  414. 

Expansion,  coefficient  of,  201,  203, 
table,  201 ;  in  freezing,  231 ;  of 
gases,  204  to  207;  of  liquids,  203, 
204  ;  of  solids,  198  to  203  ;  of  water, 
204. 

Eye,  503  to  505. 

Factor  of  safety,  155. 

Fahrenheit  scale,  196. 

Falling  bodies,  166  to  169. 

Faraday,  Michael,  285. 

Faucet,  83. 

Field,  of  generator,  380,  381 ;  magnetic, 
285  to  288,  referred  to  on  nearly 
every  page  from  371  to  425 ;  of 
motor,  385  ;  revolving,  414  to  420  ; 
rotating,  421  to  423;  side  push  of, 
383  to  385. 

Fireless  cooker,  219,  220. 

Flaming  arc,  354. 

Flatiron,  electric,  347. 

Fleming's  rule,  for  generators,  373 ; 
for  motors,  385. 


Floating  bodies,  73  to  75. 

Flux,  see  field,  magnetic. 

Flywheel,  187,  273,  289. 

Focal  length,  of  lens,  496 ;    of  mirror, 

475. 
Foci,    conjugate,   480,   498 ;    real   and 

virtual,  478. 
Focus,    principal,    of    lens,    496 ;      of 

mirror,  475,  478. 
Fog,  250. 
Foot,  5  ;    -candle,  469  ;  -candle  meter, 

469  to  471 ;  -pound,  37. 
Force,  buoyant,  73,   112;    centripetal, 

176  ;    -diagram,  132  ;    electromotive, 

312  ;   of  expansion,  199  ;    of  friction, 

54 ;     lines    of,    see   field,    magnetic ; 

moment   of,    20 ;     vs.   pressure,    60 ; 

unbalanced,  178 ;    useful  component 

of,  135. 

Force  pump,  110. 
Forces,    composition   of,    132 ;     equili- 

brant  of,  131 ;    molecular,  92 ;    non- 
parallel,    129  to   148;    parallel,   33; 

parallelogram  of,   130 ;    represented 

by  arrows,  129 ;    resolution  of,  133 ; 

resultant  of,  130. 
Fractional  distillation,  240. 
Franklin,  Benjamin,  303. 
Fraunhofer  lines,  518. 
Freezing,  by  boiling,  251 ;  evolves  heat, 

233 ;     expansion    in,    231  ;     -point, 

196,  230,  table,  231. 
Frequency,  of  alternating  current,  417  ; 

of   oscillatory   discharge,    530,    535 ; 

of  sound,  443  ;   of  water  waves,  433 ; 

in  wave  formula,  433. 
Friction,   50  to   55;    on  incline,    137; 

produces  electricity,  293 ;    produces 

heat,  195  ;  in  water  pipes,  85. 
Frost,  249. 
Fuel  oil,  268. 

Fulcrum,  16  ;   force  at,  21. 
Fundamental,  447. 
Furnace,    214,    215   (see    also    242    to 

245). 
Fuse,  347. 

Galileo,  Galilei,  103. 

Galvanometer,  344. 

Gas,   engines,   268  to  270;    equation, 

209;     meter,    128;     legal    standard 

for,  466. 


INDEX 

[References  are  to  pages.] 


549 


Gases,    electrical    discharge    through, 

536  to  540  ;  mechanics  of,  96  to  128  ; 

sound  transmitted  by,  428 ;    spectra 

of,  519  to  521  ;    thermal  properties 

of,  204  to  211. 

Gasoline  engines,  270  to  275. 
Gauge,   Bourdon,   85,    121  ;     mercury, 

84,    121 ;     steam,    259 ;     tire,    127 ; 

water,  66,  259. 
Geissler  tube,  537. 
Generator,  a.-c.,  413  to  420,  536  ;  d.-c., 

371  to  383. 
Grade,  of  incline,  41. 
Gram,     -calorie,     226;      mass,      183; 

weight,  8. 

Gramme-ring  armature,  377. 
Gravitation,  universal,  182. 
Gravity,   acceleration  of,    168;    center 

of,  23  ;   specific,  76  to  81. 

Half-time  shaft,  269. 

Heat,  2,  194  to  280 ;  conservation  of, 
218 ;  of  fusion,  233  ;  measurement 
of,  226 ;  mechanical  equivalent  of, 
277 ;  molecular  theory  of,  223 ; 
radiant,  220;  evolved  by  radium, 
542;  specific,  227,  table,  228; 
transmission  of,  211  to  222;  of 
vaporization,  241. 

Heater,  for  hot  water,  214. 

Heating,  electric,  194,  346  to  350; 
hot-air,  215 ;  hot-water,  214 ;  in- 
direct system,  216,  244  ;  steam,  242  ; 
vacuum  system,  244 ;  vapor  sys- 
tem, 244. 

Helium,  in  airships,  114  to  116;  in 
sun,  521. 

Helmholtz,  Hermann  von,  444. 

Henry,  Joseph,  340. 

Hertz,  Heinrich  Rudolf,  532. 

Hooke's  law,  152. 

Horse  power,  47 ;   h.  p.  hour,  349. 

Humidity,  247. 

Hydrant,  84. 

Hydraulic,  jack,  70;   press,  68  to  71. 

Hydraulic  analogue,  of  cell,  310;  of 
cells  in  parallel,  328 ;  of  cells  in 
series,  328 ;  of  condenser  301 ;  of 
condenser  on  a.-c.  circuit,  413 ;  of 
difference  of  potential,  308  ;  of  elec- 
trical units,  314  ;  of  voltmeter,  345. 

Hydrometer,  79,  365. 


Ice,  230  to  235  ;   -making,  252. 

Ignition  systems,  394  to  397. 

Illumination,  463  to  471. 

Image,  formed,  by  pinhole,  463,  by 
plane  mirror,  473,  by  curved  mirror, 
479,  by  lens,  497,  499,  500 ;  defects 
of,  476,  501;  size  f,  480,  481,  499; 
virtual,  479,  481,  500. 

Impedance,  410. 

Incandescent  lamp,  351  to  353;  vac- 
uum in,  99. 

Incidence,  angle  of,  472,  488. 

Inclined  plane,  40,  137,  167. 

Inclosed  arc,  354. 

Index  of  refraction,  488,  492. 

Induced,  currents,  370  to  402 ;  e.  m.  f ., 
direction  of,  372,  amount  of,  373 ; 
electrification,  298  ;  magnetism,  288. 

Inductance,  395  to  397. 

Induction,  coil,  393,  uses,  394;  ma- 
chines, 302;  motor,  421  to  423; 
electric,  298 ;  magnetic,  288. 

Inertia,  law  of,  174  to  176 ;  in  curved 
motion,  176  to  178 ;  electromagnetic, 
397. 

Infra-red  rays,  526. 

Insulators,  electric,  294,  305,  426; 
heat,  217. 

Intensity,  of  illumination,  464 ;  of  a 
lamp,  465  ;  of  sound,  437,  442. 

Interaction,  law  of,  180  to  182. 

Interference,  of  light,  525;  of  sound, 
451. 

International,  ampere,  360 ;  candle,  466. 

Inverse  squares,  law  of,  for  gravita- 
tion, 183  ;  for  illumination,  464,  469  ; 
for  magnetic  attraction  and  repul- 
sion, 282  ;  for  sound  intensity,  437. 

Ions,  358. 

Isobars,  106. 

Jackscrew,  42,  46,  47,  59. 
Joule,  the,  189,  350. 

Kelvin  (Sir  William  Thomson),  192. 

Kerosene  engine,  275. 

Key,  telegraphic,  342. 

Kilogram,    -calorie,    279;     mass,    183; 

weight,  7. 

Kilowatt,  348  ;   -hour,  349. 
Kinetic,   energy,    187  to   191 ;    theory 

of  gases,  126. 


550 


INDEX 

[References  are  to  pages.] 


Lactometer,  80. 

Lamps,  electric,  351  to  355  ;  kerosene, 
213  ;  luminous  intensity  of,  465  to 
469;  standard,  465. 

Lantern,  projecting,  505. 

Latent  heat,  of  fusion,  233 ;  of  vapori- 
zation, 241. 

Lawn  sprinkler,  268. 

Lead  storage  cell,  362. 

Left  hand  rule  (motors),  385. 

Length,  units  of  (table),  5. 

Lens,  495  to  501 ;  achromatic,  517 ; 
camera,  502 ;  crystalline,  503 :  cy- 
lindrical, 505  ;  focal  length  of,  496  ; 
formula,  498;  magnification  by, 
499,  509. 

Lenz'slaw,  371. 

Levers,  16  to  28. 

Leyden  jar,  300 ;   discharge  of,  529. 

Liberty  motor,  143. 

Lift  pump,  109. 

Lifting  magnet,  341. 

Light,  2,  463  to  528;  advances  in 
straight  lines,  463  ;  analysis  of,  by 
prism,  516 ;  distribution  of,  arourid 
lamp,  468;  electric,  351  to  355; 
electromagnetic  theory  of,  526 ; 
interference  of,  525 ;  reflection  of, 
472 ;  refraction  of,  486  to  489,  491  ; 
velocity  of,  489,  492;  wave  length 
of  (table),  522;  waves,  490,  522. 

Lightning,  303,  304 ;  rod,  303,  304. 

Lines  of  force,  286 ;  push  exerted  by, 
383 ;  wire  cutting,  372 ;  m-  <ilx<> 
field,  magnetic. 

Liquids,  buoyant  effect  of,  71  to  75; 
conduction  of  electricity  by,  310, 
357 ;  expansion  of,  203 ;  incom- 
pressibility  of,  119;  measurement  of , 
6,  86;  mechanics  of,  60  to  95, 
molecular  attractions  in,  92  ;  pumps 
for,  109  to  112;  separation  of,  177, 
178,  240;  sound  transmitted  by, 
428. 

Liter,  6. 

Locomotive,  257. 

Lodestone,  281. 

Loudness,  or  intensity  of  sound,  437, 
441,  442. 

Lubrication,  53. 

Luminescent  paint,  542. 

Lung  capacity,  97. 


Machines,  1,  15,  60;  a.-c.,  413  to  423  : 
centrifugal,  177,  178 ;  compound, 
44;  d.-c.,  371  to  391  ;  efficiency  of, 
55;  flying,  142  to  145;  hydraulic, 
68  to  70,  87  to  90,  96,  109  to  112; 
induction,  302;  pneumatic,  96, 
98,  99,  117,  118;  refrigerating,  252; 
sewing,  388  ;  simple,  15  to  59  ;  talk- 
ing, 458  to  460  ;  testing,  154  ;  ther- 
mal,' 255  to  277  ;  weighing,  8,  58,  59. 

Magdeburg  hemispheres,  101,  102. 

Magnet,  current  induced  by,  370 ; 
earth  a,  284,  electro-,  339  to  346, 
373;  field  around,  286,  292;  by 
induction,  288;  lifting,  341;  mak- 
ing a,  292 ;  permanent,  uses  of,  289 ; 
saturated,  291. 

Magnetic,  ice  attraction,  declination, 
dip,  field,  induction,  lines  of  force, 
poles,  repulsion. 

Magnetism,  281  to  292;  induced,  288; 
molecular  theory  of,  290 ;  residual, 
340. 

Magnetite,  281 ;  -arc,  354. 

Magneto,  289,  380;  field  of,  288; 
Ford,  394  ;  high-tension,  395. 

Magnifying  glass,  508. 

Magnifying  power,  of  binocular,  512, 
of  lens,  509;  of  microscope,  510; 
of  opera  glass,  512. 

Major,  scale,  454  ;   triad,  453. 

Manometer,  84,  121. 

Manometric  flames,  448. 

Mass,  1S3. 

Maximum  and  minimum  thermometer, 
198. 

Mazda  lamps,  351,  352. 

Mechanical  advantage,  28. 

Mechanical  equivalent,  of  electricity, 
350  ;  of  heat,  277  to  279. 

Mechanics,  2,  and  chaps.  II  to  IX. 

Megaphone,  438. 

Melting  point,  230,  table,  231  ,  effect 
of  pressure  on,  232. 

Mercury  arc  lamp,  355. 

Meter,  foot-candle,  469,  471 ;  gas,  128  ; 
water,  86 ,  watt-hour,  423. 

Meter,  standard,  4. 

Metric  system,  4  to  8. 

Micrometer  screw,  44. 

Microphone,  398,  531. 

Microscope,  50S,  509. 


INDEX 

[References  are  to  pages.] 


551 


Mil,  318  ;   circular,  318  ;   -foot,  319. 

Milk,  testing  of,  80. 

Mirror,  curved,  475  to  483 ;  formula, 
482  ;  parabolic,  476  ;  plane,  473. 

Mixtures,  method  of,  228,  233,  242. 

Moisture,  in  atmosphere,  246  to  250. 

Molecular  theory,  of  cohesion  and 
adhesion,  92 ;  p£-  gases,  125 ;  of 
heat,  223  ;  of  magnetism,  290. 

Molecules,  304. 

Moments,  principle  of,  20,  3  '. 

Momentum,  189. 

Monoplane,  143. 

Moon,  attracts  earth,  182 ;  eclipse  of, 
464. 

Motion,  accelerated,  158  to  173 ;  laws 
of,  174  to  185. 

Motion  pictures,  506. 

Motor,  a.-c.,  420  to  424;   commutator, 
421 ;    d.-c.,  383  to  391 ;    induction, 
421  to  423  ;  liberty,  143 ;  rule,  385 
series,  389;    shunt,  388;  Asynchron- 
ous, 421 ;   water,  88. 

Muffler,  272,  462. 

Musical,  instruments,  45J>  to  458 ; 
scale,  453  ;  tones,  442  to  449. 

Newton,  Sir  Isaac,  174. 

Nodes,  432. 

Noise,  442. 

Non-parallel  forces,  129  to  148. 

Octave,  453. 

Ohm,  312,  314. 

Ohm,  Georg  Simon,  314. 

Ohm's  law,  314,  323. 

Oil  engines,  268,  275  to  277. 

Opera  glass,  511. 

Ophthalmoscope,  476. 

Optical  instruments,  476  to  478,  486, 

502  to  512. 
Organ  pipe,  456. 
Oscillations,  of  spark,  530. 
Overtones,  447. 

Parallel,  cells  in,  328 ;    circuits,  324  to 

326 ;   forces,  33. 

Parallelogram  of  forces,  130  to  144. 
Parr  bomb  calorimeter,  230. 
Parsons  turbine,  267. 
Pascal,  Blaise,  68. 
Pascal's,  law,  68,  117;   vases,  63. 


Pelton  wheel,  87. 

Pendulum,  168,  173,  191,  201 ;  reso- 
nance of,  530. 

Penumbra,  464. 

Periscope,  513. 

Permanent  magnets,  uses  of,  289. 

Permeability,  288. 

Perpetual  motion,  193. 

Phase,  of  a.-c.,  417  to  423  ;  of  waves, 
433,  452. 

Phonodeik,  449. 

Phonograph,  458  to  460,  462. 

Photometer,  466,  467. 

Physics,  nature  and  divisions  of, 
1  to  3. 

Piano,  455,  462  ;   -player,  462. 

Pigments,  523. 

Pitch,  absolute,  462 ;  international, 
454,  462;  of  screw,  42;  of  sound, 
443. 

Plate  girders  141. 

Platform  scales,  58. 

Polarization,  331. 

Poles,  of  electromagnet,  339,  340,  341 ; 
of  generator,  379,  380,  414,  417 ;  of 
motor,  386,  391,  422 ;  of  permanent 
magnet,  281,  284,  290,  344,  370, 
371,  425. 

Polyphase  circuits,  417  to  420. 

Portraits,  Ampere,  311;  Curie,  541 ; 
Faraday,  285 ;  Franklin,  303  ;  Gali- 
leo, 103;  Helmholtz,  444;  Henry, 
340;  Hertz,  532;  Kelvin,  192; 
Newton,  174;  Ohm,  314;  Pascal, 
68  ;  Volta,  309  ;  Watt,  256. 

Potential,  difference  of,  309,  312. 

Potential  energy,  186,  187,  191. 

Pound,  avoirdupois,  8. 

Power,  47;  a.-c.,  411;  concentration 
of,  affects  society,  256,  d.-c.,  348; 
-factor,  411;  horse-,  47;  trans- 
mission of,  48,  406,  407 ;  vs.  work, 
47. 

Practical  exercises ;  accuracy,  of 
carpenter,  14,  of  machinist,  14 ; 
automobile,  acceleration  of,  173, 
c.  of  g.  of,  36;  barometer,  109; 
bell,  -circuit,  346,  electric-,  346; 
blood  pressure,  122 ;  brake  levers, 
30 ;  bridges,  148 ;  clocks,  173 ;  coal, 
230 ;  color,  -blindness,  528,  -print- 
ing, 528,  of  rainbow,  528  ;  condensers, 


552 


INDEX 

[References  are  to  pages.] 


306;  cooker,  fireless,  220,  pressure, 
246;  dampers,  225;  dams,  71; 
docks,  76 ;  door-closer,  157  ;  electric 
devices,  351 ;  flashlight,  356 ;  Ford 
engine,  275 ;  gasoline  pump,  122 ; 
headlights,  485 ;  heating  system, 
217 ;  hydrometer,  82 ;  ignition, 
system,  397,  tester,  544 ;  illumina- 
tion, 471 ;  jack,  47,  59 ;  life  pre- 
server, 76  ;  light  and  power  systems, 
334,  356  ;  lines  of  force,  292  ;  loop- 
ing the  loop.  185 ;  lung  capacity, 
97  ;  magnet,  292  ;  measurement,  14  ; 
moisture,  254 ;  muffler,  462 ;  peri- 
scope, 513  ;  perpetual  motion,  193  ; 
phonograph,  462  ;  piano,  462  ;  pitch, 
462  ;  psychrometer,  251  ;  pyrometer, 
402 ;  radio  station,  544 ;  radio- 
activity, 544  ;  range  finder,  513  ; 
rectifier,  425 ;  refrigerator,  236 ; 
sal-ammoniac  cell,  334 ;  scales, 
commercial,  14,  computing,  59 ; 
shock  absorber,  157  ;  silver  cleaned, 
361;  siphon,  112;  standard  time, 
14  ;  starter-generator,  392  ;  steam, 
engine,  264,  heating  plant,  246; 
storage  battery,  367  ;  telephone,  400  ; 
temperature  of  body,  198 ;  ther- 
mometer, 198;  transformer,  410, 
bell-ringing,  410;  vacuum  cleaner, 
100 ;  velocity  of  sound,  431 ;  vowels, 
462;  water,  -motor,  91,  in  soils,  93, 
-tanks,  71. 

Precipitation,  250. 

Pressure,  60;  absolute,  121;  air 
under,  117  to  122;  of  atmosphere, 
100  to  107 :  blood-,  122 ;  -coefficient 
of  gases,  208;  -cooker,  239;  effect 
of,  on  boiling,  237,  on  freezing,  232 ; 
by  the  gauge,  121 ;  gauges,  84,  120, 
127;  in  heavy  liquids,  61  to  66; 
standard,  238 ;  transmitted,  by  gases, 
117,  by  liquids,  67  to  71 ;  vapor-,  237. 

Primary,  of  transformer,  404. 

Printing  in  colors,  528. 

Prism,     494;      analyzes     light,      516 
-binocular,  512  ;   as  mirror,  493. 

Projectiles,  171. 

Projecting  lantern,  505. 

Propeller,  43,  144. 

Psychrometer,  251. 

Pulley,  31  to  33,  38 ;   differential,  39. 


Pumps,  for  liquids,  109  to  111  ;    tire-, 

118;  vacuum,  98,  99. 
Pyrometer,  402. 

Quality,  of  musical  tone,  444  to  448. 

Radiation,  of  heat,  217,  220  to  223; 
of  light,  521  ;  from  pitch  blende, 
540;  from  radium,  541. 

Radiators,  steam,  243. 

Radio,  station,  544 ;  telegraphy,  532 
to  534  ;  telephony,  535,  536. 

Radioactivity,  540  to  544. 

Radiometer,  221. 

Radium,  540  to  543. 

Rain,  250. 

Rainbow,  528. 

Range  finder,  515. 

Rays,  cathode,  537  to  539 ;  infra- 
red and  ultra-violet,  526 ;  light, 
472,  491;  Roentgen  or  X-,  539, 
540. 

Receiver,  telephone,  398. 

Rectifiers,  425,  531,  532. 

Refining,  of  metals,  359. 

Reflection,  of  light,  472;  of  sound, 
439,  440  ;  total,  492. 

Refraction,  486  to  489  ;  by  atmosphere, 
489 ;  in  glass,  488 ;  index  of,  488, 
492;  by  lens,  496,  517;  by  plate, 
494;  by  prism,  494,  516,  518,  522; 
reason  for,  491 ;  in  water,  486. 

Refrigerator,  234;   iceless-,  253. 

Relay,  telegraphic,  343. 

Repulsion,  electric,  295,  296,  299,  302 ; 
magnetic,  282. 

Resistance,  302,  312 ;  of  ammeter, 
345  ;  computation  of,  318  ;  of  copper 
wire,  320,  table,  321  ;  internal 
and  external,  328,  329,  332,  366; 
measurement  of,  318  ;  specific,  319  ; 
starting,  387 ;  temperature  affects, 
322;  unit  of,  312,  314;  of  volt- 
meter, 345. 

Resistances,  in  parallel,  324  ;  in  series, 
322. 

Resolution  of  forces,  133. 

Resonance,  acoustical,  445  ;  electrical, 
531 ;  of  pendulums,  530. 

Resonators,  445. 

Resultant,  130,  131. 

Retardation,  162,  165. 


INDEX 

[References  are  to  pages.] 


553 


Retina,  503. 

Reverberation,  441. 

Right    hand    rule    (generators),    373; 

see  also  thumb  rule. 
Rivet,  150. 

Roentgen  rays,  539,  540. 
Roller  bearings,  56. 
Roof  truss,  138,  139. 
Rotor,  squirrel  cage,  423. 
Ruhmkorff  coil,  394. 

S-trap,  117. 

Safety,  factor  of,  155. 

Safety  valve,  259. 

Sailboat,  141. 

Saturated  air  (table),  247. 

Scale,  musical,  453,  454. 

Scales,  computing,  59 ;  platform,  58. 

Screw,  42  to  44. 

Seaplanes,  144. 

Secondary,  of  transformer,  404. 

Self-induction,  395  ;   applications,  397. 

Series,  cells  in,  327;  circuits,  322; 
generators,  381 ;  motors,  389. 

Sewing  machine,  388. 

Sextant,  473,  474. 

Shadow,  cathode  ray,  538 ;  earth's, 
464. 

Shear,  150. 

Shock  absorber,  157. 

Shunt,  of  ammeter,  345  ;  generators, 
381 ;  motors,  388. 

Single  phase  current,  418. 

Siphon,  111;   -closet,  112. 

Siren,  443. 

Size,  apparent,  505 ;  of  image,  480, 
481,  499. 

Snow,  250. 

Soda  water,  123. 

Solar  spectrum,  518. 

Solid  injection  engine,  278. 

Solids,  conductivity  of,  electrical,  294, 
thermal,  217;  density  of,  9  to  11, 
table,  10;  sound  transmitted  by, 
428;  specific  gravity  of,  77,  78; 
spectra  of,  519  ;  thermal  expansion 
of,  198. 

Solutions,  conduction  by,  357. 

Sonometer,  455. 

Sound,  2,  427  to  462;  finding  direc- 
tion of,  438;  intensity  of,  437; 
interference  of,  451 ;  nature  of,  431, 


435,  436;  reflection  of,  439;  in 
rooms,  440  to  442 ;  sensation  of, 
431 ;  velocity  of,  429,  431. 

Sound-ranging,  439. 

Sounder,  telegraphic,  343. 

Spark,  advancing  the,  275 ;  oscilla- 
tions of,  530 ;  -plug,  272,  394. 

Sparking  voltage,  394,  536. 

Speaking  tubes,  438. 

Specific,  gravity,  76  to  81 ;  heat,  227, 
table,  228  ;  resistance,  319. 

Spectra,  516  to  521 ;  absorption,  519 : 
bright-]4ne,  519;  continuous,  519; 
solar,  518. 

Spectroscope,  517,  518. 

Spectrum  analysis,  519. 

Speed,  see  velocity. 

Speedometer,  160. 

Spyglass,  511. 

Squirrel-cage  rotor,  423. 

Stability,  25. 

Standard,  kilogram,  183;  lamp,  465; 
meter,  4 ;  pressure,  238 ;  weight, 
184. 

Starter,  automobile,  392. 

Starting,  -resistance,  387  ;  -torque,  389. 

Static  electricity,  293  to  306. 

Steam,  236  to  245  ;  boiler,  256  to  259  ; 
engine,  255,  260  to  263;  gauge, 
259;  heating,  242  to  245;  latent 
heat  of,  242 ;  turbines,  264  to  268. 

Stereopticon,  505. 

Stoker,  automatic,  258. 

Stop  watch,  13. 

Storage  batteries,  362  to  367  ;  care  of, 
365,  367;  Edison,  365;  lead,  362; 
uses,  363. 

Strain,  151,  155. 

Street-car  motor,  389. 

Strength,  breaking,  154 ;  of  materials, 
149  to  157. 

Stress,  149  to  151,  155. 

Strings,  vibrating,  447,  455. 

Submarine,  boat,  75  ;   telegraph,  343. 

Suction  pump,  109. 

Surveyor's  transit,  511. 

Sympathetic  vibrations,  444,  530. 

Tables,  accelerations,  162 ;  accelera- 
tion units,  161 ;  boiling  points,  239  ; 
coefficients  of  expansion,  201  ;  den- 
sities, 10 ;  electric  conductors  and 


554 


INDEX 

{References  are  to  pages.] 


insulators,  294  ;  electric  vs.  hydraulic 
units,  314 ;  electrochemical  equiv- 
alents, 360;  energy  units,  350; 
falling  body,  166  ;  force  units,  179  ; 
freezing  points,  231  ;  heat  values 
of  fuels,  226  ;  length  units,  5 ;  me- 
chanical equivalent  of  heat,  279 ; 
melting  points,  231  ;  moisture  in 
saturated  air,  247  ;  relation  between 
notes  of  octave,  454 ;  specific  grav- 
ities, see  densities ;  specific  heats, 
228;  speeds,  or  velocities,  158; 
volume  units,  6 ;  water  boiling  at 
various  pressures,  238  ;  wave  lengths 
of  light,  522;  weight  units,  8; 
wire  (gauge,  diameter,  area,  resist- 
ance), 321  ;  work  units,  189. 

Telegraph,  342;  radio-,  532  to  534; 
submarine,  343. 

Telephone,  398  to  400;  condenser 
used  in,  411 ;  radio-,  335,  336. 

Telescope,  astronomical,  510 ;  erect- 
ing, 511  ;  reflecting,  477,  478. 

Temperature,  absolute,  205,  206  ;  high, 
211;  low,  210;  scales,  196. 

Tension,  149,  151,  153,  154 ;  -member, 
141 ;  surface-,  91 ;  vapor-,  237. 

Terminal  voltage,  332. 

Thermoelectric  currents,  402. — 

Thermometer,  195;  calibration  of, 
238;  centigrade,  196;  clinical,  197; 
electric,  402;  Fahrenheit,  196; 
maximum  (and  minimum),  197,  198; 
mercury,  195 ;  metallic,  200 ;  re- 
cording, 200;  special  types  01,  197; 
wet-  and  dry-bulb,  248. 

Thermos  bottle,  218. 

Thermostat,  200. 

Thomson,  Sir  William,  192. 

Three-phase  current,  418. 

Throttle,  270,  275. 

Thumb  rule,  for  coil,  340  ;  for  wire,  338. 

Thunder,  303,  440. 

Time,  units  of,  13. 

Toepler-Holz  machine,  302. 

Toggle-joint,  148. 

Torque,  152;  on  armature,  385; 
starting-,  389. 

Torricelli's  experiment,  101. 

Tractor,  275,  276. 

Trajectory,  171. 

Transformer,  403  to  408,  410. 


Transmission,  of  electric  power,  406, 
407;  of  electric  waves,  526,  527, 
535;  of  heat,  211  to  222;  of  light, 
490 ;  of  mechanical  power,  48 ;  of 
sound,  428,  429,  490. 

Transmitter,  radio,  535 ;  telephone, 
399. 

Trap,  117. 

Triad,  major,  453. 

Truss,  bridge,  140;   roof,  138,  139. 

Tungar  rectifier,  425. 

Tungsten  lamp,  351,  352. 

Tuning  fork,  427,  429,  445,  446,  451. 

Turbine,  steam,  264  to  268;  water, 
88  to  90. 

Twisting,  150,  152. 

Two-phase  current,  418. 

Ultra-violet  rays,  526. 

Umbra,  464. 

Unbalanced  force,  178. 

Underfeed  stoker,  258. 

Uniflow  steam  engine,  262,  263. 

Units,  4 ;  of  acceleration,  161 ;  of 
area,  5 ;  consistent,  165,  179 ;  of 
current,  311,  360;  of  density,  10; 
of  electric  quantity,  311  ;  electric 
vs.  hydraulic  (table),  314  ;  of  e.  m.  f., 
313  ;  of  energy,  189,  350 ;  of  force, 
179  ;  of  heat,  226,  227  ;  of  illumina- 
tion, 469  ;  of  kinetic  energy,  189 ; 
of  length,  4,  5  ;  of  light  intensity, 
466;  of  mass,  183;  of  power,  47, 
348,  391;  of  pressure,  60;  of  re- 
sistance, 312,  319 ;  of  time,  13 ;  of 
velocity  or  speed,  158  ;  of  volume,  6 ; 
of  weight,  7,  8,  183;  of  work,  37, 
189,  278,  279. 

Universal  gravitation,  182. 

Vacuum,  98;  bottle,  218;  cleaning, 
99,  100;  in  dispatch  tubes,  99; 
electric  discharge  in,  537  to  540 ; 
gauge,  122;  in  incandescent  lamp 
bulbs,  99,  352;  "nature  abhors," 
101;  pans,  238;  partial,  98;  per- 
fect, 98;  pumps,  98,  99;  radiant 
heat  transmitted  by,  220 ;  sound 
not  transmitted  by,  428 ;  -tube 
detector,  532;  -tube  rectifier,  425; 
weight  in,  113. 

Vapor  pressure,  or  tension,  237. 


INDEX  555 

[References  are  to  pages.] 

Velocity,  or  speed,    158    to  160,  table,        491  ;      seeing     under.     504 ;     sound 

158  ;    of  light,  489  to  492  ;    of  mole-        transmitted  by,  428  ;   total  reflection 

cules,    125;     -ratio,    45;     of    sound,        in,  493 ;    -tube  boiler,  257 ;  turbines, 

429  to  431 ;   in  wave  equation,  433.          88  to  90  ;    velocity  of  light  in,  492  ; 

Ventilation,  215.  velocity  of  sound  in,   430 ;    waves, 

Vibration,  of  air  columns,  457  ;   audible        432  ;   wheels,  87  ;   works,  82  to  84. 

limits  of,  443,  449 ;    of  diaphragms,    Watt,    348,    391 ;     -hour    meter,    423, 

398,    399,    459,    460 ;     forced,    446 ;        424 ;   -second,  350. 

frequency    of,    433,    443 ;     of    light,    Watt,  James,  256. 

521;      longitudinal,    434,    435;      of    Wave,  -front,  491,  497 ;    -length,  433, 

membranes,  458;    sound  caused  by,        of     light,      516,     521,     table,    522; 

427  ;   of  strings,  447,  455,  456  ;   sym-        -formula,  433,  436. 

pathetic,    444    to    446  ;     of    tuning    Waves,  electric,  529  to  536  ;  light,  490, 

fork,    427    to    429;     made    visible,        527;     sound,   431,    435;     transverse 

398,  427/528,  435  ;   in  waves,  432.  and  longitudinal,  433  ;   water,  432. 

Virtual,  focus,  478;    image,  479,  481,    Weather,  105,  106;   -map,  107. 

•TOO,  510.  Wedge,  41 ;   rotating,  42. 

Visual  angle,  505.  Weighing  machines,  8?  58,  59. 

Voice,  458,  462.  Weight,    of   air,    96;    local,    183;     vs. 

Volt,  313.  mass,     183 ;      standard,     183,     184 ; 

Volta,  Alessandro,  309.  units  of,  7,  table,  8;  in  vacuum,  113. 

Voltage,  see  electromotive  force.  Welding,  electric,  406. 

Voltmeter,  317,  345.  Wet-  and  dry-bulb  thermometer,  248. 

Volume,  of  air,  96 ;  units  of,  6.  Wheel  and  axle,  30,  36,  37,  45. 

Vowels,  462.  Wimhurst  machine,  302. 

Windlass,  30,  31. 
Watch,  balance  wheel  of,  202;    stop-,    Wire  table,  321. 

13.  Wireless,     telegraphy,     532    to    534; 

Water,  8,  60  to  95,  109  to  112,  226  to        telephony,  535,  536. 

254;    absorption  of  gases  by,    123;    Work,  definition  of,  36,  47;    electric, 

-closet,    112;    in   steam    condenser,        349;  vs.  power,  47 ;   principle  of,  37, 

261 ;    a  poor  conductor,   294  ;    cur-        55  ;   units  of,  37,  189,  278,  279. 

rents,  307  to  316 ;    density    of,   10 ;    Worm  gear,  44. 

distilled,    239,    240;    electrolysis   of, 

357  ;     energy    of,   186  ;    -equivalent,    X-ray  tube,  vacuum  in,  99. 

229  ;     expansion    of,    204 ;     -gauge,    X  rays,  539,  540. 

66,  259;    heat  of    freezing  of,  233, 

234;    heat  of  vaporization  of,  241,    Yard,  U.  S.  legal,  5. 

242;      heating    system,     214,     215; 

meter,  86;   motor,  88,  91 ;   pressure,    Zeppelin,  114. 

84 ;   refraction  of  light  by,  487,  488,    Zero,  absolute,  206. 


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